Chapter 6: Heat and Energy
In 1798, in the military workshops at Munich, an army officer named Benjamin Thompson — later known as Count Rumford — stood watching brass cannon being bored out. A blunt steel borer was pressed against the metal and turned by horses, hour after hour. The metal shavings that curled away were so hot that the workers could not hold them.
Everyone at the time believed heat was an invisible fluid, squeezed out of the metal by the cutting. Rumford was not convinced. If heat were a fluid stored inside the brass, the supply should run out. So he set up a careful test. He surrounded the cannon barrel with a wooden box, filled the box with cold water, and let the horses turn the borer.
After about two and a half hours, with nothing burning anywhere near it, the water boiled.
Rumford saw what this meant. As long as the horses kept working, heat kept appearing. It had no limit because it was not being released from anywhere — it was being made, out of the work the horses were doing. Heat, he argued, is not a substance at all. It is something a body has because its particles are moving.
It took another fifty years for physicists to settle the matter in Rumford’s favour. When they did, heat took its place alongside motion, electricity and chemical change as one more form of a single quantity: energy.
Diagram
Fig. 6.0-1 — Rumford’s Cannon-Boring Experiment Cutaway side view of a horizontal brass cannon barrel held in a wooden trough filled with water; a blunt steel borer is pressed into the open end of the barrel and turned by a horizontal shaft driven by a pair of horses walking in a circle; show steam rising from the water surface. Label the cannon barrel, the blunt borer, the wooden box of water, the drive shaft and the horses. Add a small arrow at the borer marked ‘work done against friction’ and a small arrow at the water marked ‘heat produced’.
6.1 Concept Of Heat
You already know several forms of energy — the energy of a moving body, the energy stored in a stretched spring, the energy carried by an electric current. This section adds one more to that list, and it is the one you meet most often in daily life.
6.1.1 Heat As A Form Of Energy
Rub your palms briskly against each other and they grow warm. Pass an electric current through a metallic wire and the wire gets hot. Burn coal and you get warmth from the fire. Pump air into a bicycle tube and the barrel of the pump becomes hot to touch. These four everyday situations are drawn in Fig. 6.1-1.
Diagram
Fig. 6.1-1 — Four Everyday Ways Of Producing Heat Four small panels in a row, each a simple line drawing with a small ‘hot’ symbol (short wavy lines) at the place that becomes warm. Panel 1: a pair of palms being rubbed together. Panel 2: a length of metallic wire connected across a cell, with the wire glowing. Panel 3: lumps of coal burning in a stove. Panel 4: a hand-operated bicycle pump connected to a tyre, with the barrel marked as warm. Label the four panels: rubbing palms, current in a wire, burning coal, pumping air into a tube.
Look at what is happening in each case. In the first and the fourth, you are doing work — your muscles push, and heat appears. In the second, electrical energy is being supplied; in the third, chemical energy stored in the coal is being released.
So heat is produced either by doing work, or by supplying energy in some other form. Energy is not created in any of these cases — it is only changed from one form into another. This tells us something important: heat is itself a form of energy.
Flowchart
FC 6.1 — How Heat Is Produced From Other Forms Of Energy Mechanical energy (rubbing palms, pumping air) → increased random motion of the molecules of the body → heat Electrical energy (current in a wire) → increased random motion of the molecules of the body → heat Chemical energy (burning coal) → increased random motion of the molecules of the body → heat
6.1.2 Internal Energy And The Flow Of Heat
Every body is made up of molecules. These molecules are in a state of random motion, and each molecule also exerts a force of attraction on its neighbours. Because they move, the molecules have kinetic energy; because they attract one another, they also have potential energy.
The total of these two, added up over all the molecules of a body, is called the internal energy of the body. The heat energy of a body is the internal energy of its molecules. A hot body has more internal energy than an identical cold body at a lower temperature.
Now place a hot body in contact with a cold body. After some time the cold body has warmed up and the hot body has cooled down. The internal energy of the cold body has increased and that of the hot body has decreased.
Nothing has been created or destroyed here. Energy has simply been transferred from the hot body to the cold body. Heat is the name we give to the energy that flows in this way — from a body at a higher temperature to a body at a lower temperature.
Why Things Feel Hot Or Cold
This also explains what your skin is telling you. A body feels hot when heat energy flows from that body into your hand. It feels cold when heat energy flows out of your hand into the body.
If you touch an iron chair that has been standing in sunlight, heat passes from the chair to your hand, and the chair feels hot. If you touch a cube of ice, heat passes from your hand to the ice, and the ice feels cold. In both cases your skin is reporting the direction of flow, not the amount of energy present.
Diagram
Fig. 6.1-2 — Flow Of Heat From A Hot Body To A Cold Body Two rectangular blocks touching along one face. The left block is labelled ‘hot body, higher temperature’ and drawn with widely spaced dots moving fast (short motion arrows on the dots); the right block is labelled ‘cold body, lower temperature’ with dots moving slowly (shorter motion arrows). A broad arrow across the contact face points from left to right and is labelled ‘heat’. Add captions below the blocks: ‘internal energy decreases’ under the left block and ‘internal energy increases’ under the right block.
6.1.3 Units Of Heat
Heat is a form of energy, so it is measured in the same units as energy. The SI unit of heat is the joule, written J and named after the physicist James Prescott Joule. In the CGS system the unit of heat is the erg, and the two are related as
\[1\\ \\text{J} = 10^{7}\\ \\text{erg}\]
Heat is also measured in an older unit called the calorie (cal), and in the larger kilocalorie (kcal), where
\[1\\ \\text{kcal} = 1000\\ \\text{cal}\]
The calorie and the joule are two units for the very same quantity, so a fixed number connects them:
\[1\\ \\text{cal} = 4.186\\ \\text{J}\\ (\\text{or nearly } 4.2\\ \\text{J})\]
To go from calorie to joule you multiply by \(4.186\); to come back the other way you divide by it. Since these are units of the same quantity, the amount of heat has not changed at all — only the unit in which we state it.
6.2 Concept Of Temperature
In the last section heat always flowed one way — from the hot body to the cold one. The quantity that decides which body is ‘the hot one’ is temperature, and it is worth looking at carefully, because it is not the same thing as heat.
6.2.1 Temperature And The Direction Of Heat Flow
Keep a hot body in contact with a cold body and watch what happens. After some time the hot body has become less hot and the cold body has become less cold. This is simply the flow of heat from the hot body to the cold body.
The body that gives out heat is said to be at a higher temperature, and the body that receives it at a lower temperature. So temperature is the quantity that determines the direction in which heat flows.
When a body receives heat energy, the particles that make it up start vibrating more vigorously, and the temperature of the body rises. This holds provided the physical state of the body and its dimensions remain unchanged — heat supplied to melting ice, for instance, changes its state instead of raising its temperature.
Same Temperature, Not Same Heat
Suppose two bodies are placed in contact and no heat flows between them at all. We then say the two bodies are at the same temperature. But this does not mean that they contain the same amount of heat.
Temperature by itself never tells us how much heat energy a body contains. Experiment shows this plainly: give the same quantity of heat to different bodies and they warm up by different amounts. The heat energy contained in a body depends on its mass, its temperature and the nature of the material it is made of.
Think of a cup of boiling water and a bucket of boiling water. Both are at \(100\\ ^\\circ\\text{C}\), so no heat flows between them. Yet the bucket holds far more heat, because it holds far more water.
6.2.2 Units And Scales Of Temperature
The SI unit of temperature is the kelvin, symbol K. The two other units in common use are the degree celsius, symbol \(^\\circ\\text{C}\), and the degree fahrenheit, symbol \(^\\circ\\text{F}\).
A scale of temperature is fixed by choosing two temperatures that can be reproduced anywhere. The two chosen are the ice point, the temperature of melting ice, and the steam point, the temperature of steam above water boiling at normal atmospheric pressure. Fig. 6.2-1 shows where these two points fall on all three scales.
Diagram
Fig. 6.2-1 — The Ice Point And The Steam Point On Three Scales Three vertical thermometer scales drawn side by side and aligned horizontally, labelled Celsius scale, Fahrenheit scale and Kelvin scale. Draw a horizontal dashed line across all three at the lower level, labelled ‘ice point’, meeting the scales at 0 °C, 32 °F and 273 K. Draw a second horizontal dashed line across all three at the upper level, labelled ‘steam point’, meeting the scales at 100 °C, 212 °F and 373 K. Between the two dashed lines mark the number of equal divisions on each scale: 100 on the Celsius scale, 180 on the Fahrenheit scale, 100 on the Kelvin scale.
Relating The Celsius And Kelvin Scales
A degree on the Kelvin scale is exactly equal in size to a degree on the Celsius scale. The two scales differ only in where their zero is placed, so converting between them means adding or subtracting a fixed number:
\[t\\ \\text{K} = 273 + t\\ ^\\circ\\text{C}\]
where the left side is the temperature on the Kelvin scale in K, and \(t\) on the right is the same temperature on the Celsius scale in \(^\\circ\\text{C}\). (More precisely the number is \(273.15\).) In words: add 273 to the temperature in degree celsius to get the temperature in kelvin.
The zero of the Kelvin scale, \(0\\ \\text{K}\), is called absolute zero. It lies at \(-273\\ ^\\circ\\text{C}\), and it is the temperature at which molecular motion would cease and the pressure and the volume of a gas would fall to zero. No body can be colder than this, so a negative temperature is not possible on the Kelvin scale.
Relating The Celsius And Fahrenheit Scales
Between the ice point and the steam point there are 100 equal degrees on the Celsius scale and 100 on the Kelvin scale, but 180 equal divisions on the Fahrenheit scale. So one Celsius degree covers the same interval as \(\\tfrac{9}{5}\) of a Fahrenheit degree — the Fahrenheit degree is the smaller step.
The two scales also start counting from different places, since the ice point is \(0\\ ^\\circ\\text{C}\) but \(32\\ ^\\circ\\text{F}\). Both facts together give
\[\\frac{C}{5} = \\frac{F - 32}{9}\]
where \(C\) is the temperature in \(^\\circ\\text{C}\) and \(F\) is the same temperature in \(^\\circ\\text{F}\). The 32 subtracted from \(F\) shifts the starting point; the 5 and the 9 look after the different sizes of the degrees.
6.2.3 Heat Compared With Temperature
Heat and temperature are closely linked, but they are different quantities with different units and different meanings. Table 6.1 sets them side by side.
Reading the last row is a good test of whether the difference has landed. Heats add up; temperatures do not. Mix a mug of water at \(30\\ ^\\circ\\text{C}\) with an equal mug at \(50\\ ^\\circ\\text{C}\) and you get water somewhere between the two, never at \(80\\ ^\\circ\\text{C}\).
6.3 Thermal Expansion
Heating a body raises the temperature of the body, and it usually does one more thing besides: it makes the body bigger. Almost all substances — solids, liquids and gases alike — expand on heating and contract on cooling.
The reason lies in the molecules. On heating, the molecules of a substance vibrate more vigorously about their positions, and the average distance between neighbouring molecules increases a little. Multiply that tiny increase by the vast number of molecules in a body, and the body as a whole grows measurably larger.
6.3.1 The Three Kinds Of Thermal Expansion
A solid has a definite shape. So when a solid is heated, it expands in every direction at once — its length, its area and its volume all increase together. We give each of these three increases its own name, as shown in Fig. 6.3-1.
The increase in length is called linear expansion. The increase in area is called superficial expansion. The increase in volume is called cubical expansion.
Diagram
Fig. 6.3-1 — The Three Kinds Of Expansion In A Solid Three panels in a row, each showing a solid before heating in solid outline and after heating in dashed outline slightly larger, with small outward arrows. Panel 1: a long thin rod, with the extra length marked at one end; label ‘linear expansion — increase in length’. Panel 2: a flat rectangular plate, with the extra width and length marked on two sides; label ‘superficial expansion — increase in area’. Panel 3: a cube, with the extra size marked on three edges; label ‘cubical expansion — increase in volume’. Add a heading strip above the row: ‘a solid expands in all directions on heating’.
Liquids and gases are different. They have no definite shape of their own, so length and area mean nothing for them — they take the shape of whatever holds them. A liquid or a gas can therefore show only cubical expansion, also called volumetric expansion.
How Much Each State Expands
The three states of matter do not expand equally for the same rise in temperature. On heating, liquids expand more than solids, and gases expand much more than liquids.
This follows from how tightly the particles are held. In a solid the molecules are locked closely together by strong forces, so they can be pushed apart only slightly. In a liquid the hold is looser, and in a gas the molecules are barely held at all, so a gas is free to swell a great deal.
6.3.2 Substances That Contract On Heating
‘Almost all substances’ is not the same as ‘all’. A few substances behave the other way round over a certain range of temperature: they contract when heated and expand when cooled.
Three of them are worth naming. Water does this from \(0\\ ^\\circ\\text{C}\) to \(4\\ ^\\circ\\text{C}\). Silver iodide does it from \(80\\ ^\\circ\\text{C}\) to \(141\\ ^\\circ\\text{C}\). Silica does it below \(-80\\ ^\\circ\\text{C}\).
Notice that each of these is stated with a temperature range attached. Outside that range the substance behaves normally, expanding on heating like everything else. The odd behaviour belongs to the range, not to the substance for all time.
The expansion of a substance on cooling it within a certain range of temperature is called anomalous expansion of that substance. Of the three, water matters far more than the others, and the rest of this part of the chapter is about it.
6.4 Anomalous Expansion Of Water
Take some water at \(0\\ ^\\circ\\text{C}\) and start heating it. Instead of expanding, as you would now expect, it contracts. It goes on contracting all the way up to \(4\\ ^\\circ\\text{C}\). Heat it further above \(4\\ ^\\circ\\text{C}\) and it expands normally.
Now run the same thing backwards. Take water at a temperature above \(4\\ ^\\circ\\text{C}\) and cool it. It contracts, as any substance would, until the temperature reaches \(4\\ ^\\circ\\text{C}\). Cool it further, from \(4\\ ^\\circ\\text{C}\) down to \(0\\ ^\\circ\\text{C}\), and it expands.
That last step is the strange one, and it is the one that gets the name.
6.4.1 Variation Of Volume Of Water With Temperature
The clearest way to see all of this at once is on a graph. Fig. 6.4-1 shows how the volume of \(1\\ \\text{g}\) of water changes as its temperature is taken from \(0\\ ^\\circ\\text{C}\) to \(10\\ ^\\circ\\text{C}\).
Diagram
Fig. 6.4-1 — Variation In Volume Of Water In The Range 0 °C To 10 °C Line graph. X-axis: temperature in °C, marked 0, 2, 4, 6, 8, 10. Y-axis: volume of 1 g of water in cm³, marked 0.9999, 1.0000, 1.0001, 1.0002, 1.0003. Draw a smooth curve that falls from a value just above 1.0000 at 0 °C to a minimum of exactly 1.0000 at 4 °C, then rises steadily and increasingly steeply to about 1.0003 at 10 °C. Add a dashed horizontal line from 1.0000 on the Y-axis and a dashed vertical line from 4 on the X-axis, meeting at the lowest point of the curve. Mark that point ‘minimum volume at 4 °C’.
The curve falls first and rises afterwards. Falling means the volume is decreasing, so the water is contracting as it is heated from \(0\\ ^\\circ\\text{C}\) to \(4\\ ^\\circ\\text{C}\). Rising means the volume is increasing, so the water expands normally on being heated from \(4\\ ^\\circ\\text{C}\) to \(10\\ ^\\circ\\text{C}\).
The turning point sits at \(4\\ ^\\circ\\text{C}\). The volume of water is therefore minimum at \(4\\ ^\\circ\\text{C}\), and for \(1\\ \\text{g}\) of water that minimum volume is \(1.0000\\ \\text{cm}^3\).
6.4.2 Variation Of Density Of Water With Temperature
The density of a substance is its mass per unit volume, measured in \(\\text{kg m}^{-3}\) in SI units and often in \(\\text{g cm}^{-3}\) for water. Since the mass of our sample of water is fixed, squeezing it into a smaller volume must make it denser, and letting it swell must make it less dense.
So the density graph is simply the volume graph turned upside down. Where the volume is least, the density is greatest. Fig. 6.4-2 shows it.
Diagram
Fig. 6.4-2 — Variation In Density Of Water In The Range 0 °C To 10 °C Line graph. X-axis: temperature in °C, marked 0, 2, 4, 6, 8, 10. Y-axis: density of water in g cm⁻³, marked 0.9996, 0.9997, 0.9998, 0.9999, 1.000. Draw a smooth curve that rises from just below 1.000 at 0 °C to a maximum of exactly 1.000 at 4 °C, then falls steadily and increasingly steeply to about 0.9997 at 10 °C. Add a dashed horizontal line from 1.000 on the Y-axis and a dashed vertical line from 4 on the X-axis, meeting at the highest point of the curve. Mark that point ‘maximum density at 4 °C’.
Follow the curve while heating. Starting at \(0\\ ^\\circ\\text{C}\), the density of water first increases up to \(4\\ ^\\circ\\text{C}\), and then decreases from \(4\\ ^\\circ\\text{C}\) to \(10\\ ^\\circ\\text{C}\).
Follow it while cooling and you trace the same curve the other way. Cooling water from \(10\\ ^\\circ\\text{C}\), the density first increases up to \(4\\ ^\\circ\\text{C}\), and then decreases as the water is cooled further from \(4\\ ^\\circ\\text{C}\) to \(0\\ ^\\circ\\text{C}\).
Either way, the peak is at the same place. The density of water is maximum at \(4\\ ^\\circ\\text{C}\), and its value there is \(1\\ \\text{g cm}^{-3}\), which is the same as \(1000\\ \\text{kg m}^{-3}\).
6.5 Hope’s Experiment On The Anomalous Expansion Of Water
The graphs of the last section were drawn from measurements. Somebody had to make those measurements, and the neatest way of showing that water is densest at \(4\\ ^\\circ\\text{C}\) was worked out more than two hundred years ago.
In 1805, the Scottish chemist Thomas Charles Hope devised a simple arrangement, now known as Hope’s apparatus, for demonstrating the anomalous expansion of water. What makes it clever is that it needs no measurement of volume or density at all — only two thermometers and some patience.
6.5.1 Hope’s Apparatus
The apparatus is drawn in Fig. 6.5-1. It consists of a tall metallic cylinder with two side openings — \(P\) near the top and \(Q\) near the bottom — fitted with thermometers \(T\_1\) and \(T\_2\) respectively.
The central part of the cylinder is surrounded by a cylindrical trough containing a freezing mixture of ice and salt. Salt lowers the melting point of ice, so this mixture stays well below \(0\\ ^\\circ\\text{C}\) and cools the middle of the cylinder strongly.
The cylinder is filled with pure water at room temperature. The temperature recorded by both thermometers is then observed at regular intervals of time.
Diagram
Fig. 6.5-1 — Hope’s Apparatus Vertical cross-section of a tall metallic cylinder filled with water, shown by close horizontal shading lines. Near the top, a side opening P carries a thermometer T₁ inserted horizontally into the water, with its reading shown as 0 °C. Near the bottom, a side opening Q carries a thermometer T₂ inserted horizontally, with its reading shown as 4 °C. Around the middle third of the cylinder, draw a wide cylindrical trough packed with a stippled mixture. Label: thermometer T₁, thermometer T₂, opening P, opening Q, water, freezing mixture of ice and salt, trough, metallic cylinder.
6.5.2 Observations
Three things are seen, one after the other.
- Initially both the thermometers \(T\_1\) and \(T\_2\) show the same temperature, that is, room temperature.
- First the temperature recorded by the lower thermometer \(T\_2\) starts decreasing, and finally it becomes steady at \(4\\ ^\\circ\\text{C}\). During this time the temperature recorded by the upper thermometer \(T\_1\) remains almost unchanged.
- While the temperature recorded by \(T\_2\) remains constant at \(4\\ ^\\circ\\text{C}\), the upper thermometer \(T\_1\) shows a continuous fall in temperature up to \(0\\ ^\\circ\\text{C}\), and then it too becomes steady.
Thus finally the temperature recorded by the upper thermometer \(T\_1\) is \(0\\ ^\\circ\\text{C}\) and that recorded by the lower thermometer \(T\_2\) is \(4\\ ^\\circ\\text{C}\).
Notice the order of events. The bottom of the cylinder cools first and stops at \(4\\ ^\\circ\\text{C}\); the top cools afterwards and goes all the way to \(0\\ ^\\circ\\text{C}\). Explaining that order is the whole point of the experiment.
6.5.3 Explanation Of The Observations
Before following the explanation, one idea is needed. In a liquid, heat is carried about by convection — the warmer, lighter part of the liquid rises and the cooler, denser part sinks, so the liquid itself moves and carries its energy with it.
Initially the water in the cylinder is at room temperature, say \(12\\ ^\\circ\\text{C}\). This is the starting point \(A\) of the graphs in Fig. 6.5-2.
The First Stage: The Bottom Cools To 4 °C
As the freezing mixture cools the water in the central portion of the cylinder, that water contracts and its density increases. Being denser, the cooled water sinks to the bottom, and warmer water from the bottom rises up to take its place.
Thus, by convection, the water in the lower part of the cylinder cools, and the reading of the lower thermometer \(T\_2\) falls rapidly. The reading of the upper thermometer \(T\_1\) does not change, because the temperature — and therefore the density — of the water in the upper part has not yet altered.
This continues till the temperature of the entire body of water below the central portion reaches \(4\\ ^\\circ\\text{C}\). This stage is shown by the part \(AB\) in graphs (a) and (b). The reading of \(T\_2\) now becomes steady, because water at \(4\\ ^\\circ\\text{C}\) is the densest there is and no colder water can sink below it.
The Second Stage: The Top Cools To 0 °C
On further cooling below \(4\\ ^\\circ\\text{C}\), the water of the central portion now expands, because of anomalous expansion. Its density therefore decreases, and instead of sinking it rises up.
To take its place, water from the top descends. By convection the water above the central portion now cools, so the reading of the upper thermometer \(T\_1\) falls rapidly till it reaches \(0\\ ^\\circ\\text{C}\), and water near the top freezes to form ice at \(0\\ ^\\circ\\text{C}\). The thermometer \(T\_1\) now shows the steady temperature \(0\\ ^\\circ\\text{C}\), shown by the part \(BC\) in graphs (a) and (b).
At this stage the lower thermometer \(T\_2\) shows the temperature \(4\\ ^\\circ\\text{C}\), at which water has its maximum density, while the upper thermometer \(T\_1\) shows the temperature of water and ice at \(0\\ ^\\circ\\text{C}\).
Flowchart
FC 6.2 — The Sequence Of Events In Hope’s Experiment Freezing mixture cools the water at the centre → this water contracts and its density increases → it sinks to the bottom → lower thermometer T₂ falls rapidly while T₁ stays unchanged → all water below the centre reaches 4 °C and T₂ becomes steady → further cooling below 4 °C makes the central water expand and its density decrease → this water now rises to the top → upper thermometer T₁ falls rapidly to 0 °C → ice forms at the top and T₁ becomes steady, with T₂ at 4 °C and T₁ at 0 °C
Diagram
Fig. 6.5-2 — Variation In Temperature With Time Recorded By The Thermometers Two line graphs side by side, each with X-axis ‘time in minutes’ (no numbers needed) and Y-axis ‘temperature in °C’ marked 0, 4 and 12. Graph (a), titled ‘temperature–time graph for thermometer T₁’: the line starts at 12 °C at point A, runs almost flat and slightly falling to point B, then falls steeply to 0 °C and continues flat along the 0 °C level to point C. Mark and label the points A, B and C, and the level 12 °C as ‘room temperature’. Graph (b), titled ‘temperature–time graph for thermometer T₂’: the line starts at 12 °C at point A, falls steeply to 4 °C at point B, then runs flat along the 4 °C level to point C. Mark and label A, B, C, the 4 °C level with a dashed horizontal line, and the level 12 °C as ‘room temperature’.
6.6 Consequences Of Anomalous Expansion Of Water
A few thousandths of a cubic centimetre, spread over a range of four degrees, sounds like a detail too small to matter. It is not. The anomalous expansion of water decides whether fish live through a winter, and whether the water pipes of a cold town survive one.
6.6.1 Survival Of Aquatic Life In Very Cold Weather
In cold weather, when the atmospheric temperature starts falling below \(0\\ ^\\circ\\text{C}\), the water at the surface of a pond or a lake — initially at a temperature above \(4\\ ^\\circ\\text{C}\) — begins to radiate heat to the atmosphere. So the temperature of the water near the surface starts falling.
When the temperature of the water at the surface falls to \(4\\ ^\\circ\\text{C}\), that water contracts and its density increases, and therefore it sinks to the bottom. Warmer water rises to take its place, cools in turn, and sinks as well. This continues till the temperature of the entire body of water reaches \(4\\ ^\\circ\\text{C}\).
Now comes the turn. Further cooling of the top layers below \(4\\ ^\\circ\\text{C}\) results in expansion of the water, and so its density decreases. As a result this water does not sink further, but remains on the surface.
Ice Forms At The Top, And Stays There
When the temperature of the atmosphere falls below \(0\\ ^\\circ\\text{C}\), the water on the surface loses further heat to the atmosphere and gradually freezes into ice. But the water below the ice layer remains at \(4\\ ^\\circ\\text{C}\), and the water layer just below the ice, in contact with it, will be at \(0\\ ^\\circ\\text{C}\). Fig. 6.6-1 shows the formation of ice at the surface of a pond.
Diagram
Fig. 6.6-1 — Formation Of Ice At The Top Of A Pond Vertical cross-section of a pond with sloping banks. Above the water, label the region ‘atmosphere below 0 °C’. Across the top of the water draw a hatched layer labelled ‘ice at 0 °C’. Immediately below the ice, mark a thin layer of water labelled 0 °C. Show the body of water below it with stippled shading labelled ‘water’, and mark the layer at the bottom of the pond as 4 °C. Draw a small fish swimming in the lower part of the water.
Ice is a poor conductor of heat. So once a sheet of ice has formed, it prevents the flow of heat from the water of the pond to the atmosphere, and the water underneath is protected from cooling further.
Thus the temperature of the water in contact with the ice is \(0\\ ^\\circ\\text{C}\), while the temperature of the water layers below the ice gradually increases to \(4\\ ^\\circ\\text{C}\) towards the bottom. Fish and other aquatic creatures remain alive in the water of the pond, though the water on the surface has frozen into ice. Nature thus protects aquatic life during the winter season.
6.6.2 Bursting Of Water Pipelines And Damage To Crops
On winter nights, as the atmospheric temperature starts falling below \(4\\ ^\\circ\\text{C}\), the water in pipelines expands. Water expanding inside a closed metal pipe has nowhere to go, so it exerts a large pressure on the walls of the pipe, and the pipes burst.
Plants suffer for the same reason. The water inside their fine capillaries expands when it falls below \(4\\ ^\\circ\\text{C}\), the capillaries burst, and the plant dies.
To protect the plants, fields are filled with water. The water in the field must give out a great deal of heat before it can freeze, and while it is freezing its temperature cannot fall below \(0\\ ^\\circ\\text{C}\). The field is therefore held near \(0\\ ^\\circ\\text{C}\) instead of dropping to the far lower temperature of the night air.
Diagram
Fig. 6.6-2 — Why A Water Pipe Bursts In Winter Two panels showing the same short length of horizontal metal pipe in cross-section. Panel 1, labelled ‘water above 4 °C’: the pipe is full of water shown by even stippling, and the pipe wall is intact. Panel 2, labelled ‘water cooled below 4 °C’: the water has expanded and turned partly to ice, shown by hatching; draw outward arrows from the ice against the inside of the pipe wall, labelled ‘large pressure on the walls’, and show a split running along the top of the pipe labelled ‘pipe bursts’.
6.7 Greenhouse Effect
The first half of this chapter followed heat as it moved between bodies in contact. Heat also travels a second way — as radiation, which needs no contact and no material at all to cross. That is how the sun’s energy reaches us, and it is where the rest of the chapter begins.
6.7.1 Solar Radiation And The Earth’s Atmosphere
The radiations coming from the sun are of many kinds. Some are high energy radiations — gamma rays, X-rays and ultraviolet rays. Others are low energy radiations — visible light, infrared radiation and radio waves.
The earth’s atmosphere does not let all of these through. It is transparent only to visible light and to infrared radiation of short wavelength. Gamma rays, X-rays and ultraviolet rays are absorbed by the ozone layer surrounding the earth, while infrared radiation of long wavelength and radio waves are turned back into space by the uppermost layer of the atmosphere, the ionosphere.
The radiations that do travel through the atmosphere are absorbed by the clouds, by the earth’s surface and by sea water. The earth’s surface is heated up in this way.
The Return Journey Is Blocked
A warm body radiates. Having been heated, the earth’s surface now radiates energy of its own — infrared radiation of long wavelength, because the surface is far cooler than the sun.
For these long wavelength radiations the earth’s atmosphere is not transparent but opaque. They are reflected back by the clouds and absorbed by the gases present above the earth’s surface. So the clouds and the gases prevent the long wavelength infrared radiations from escaping into space, and keep the earth’s surface warm. Fig. 6.7-1 shows the whole journey.
Diagram
Fig. 6.7-1 — The Greenhouse Effect Wide landscape view. Along the bottom draw the earth’s surface, with a polar ice-cap at the left end. Draw a horizontal band across the upper part labelled ‘earth’s atmosphere’, and a higher horizontal band labelled ‘ionosphere’. From the top left, draw slanting arrows down towards the earth in two groups: one group labelled ‘radio waves and infrared radiations of long wavelength from the sun’, shown striking the ionosphere and bouncing back upwards; a second group labelled ‘visible light and infrared radiations of short wavelength’, shown passing straight through the atmosphere and reaching the surface. Draw a cloud in the middle of the atmosphere band. From the earth’s surface draw wavy arrows rising, labelled ‘long wavelength infrared radiation from the earth’s surface’; show these wavy arrows being turned back downwards by the cloud and by a row of small gas molecules, labelled ‘greenhouse gases trap the heat energy’.
6.7.2 Greenhouse Gases And Their Warming Effect
The gases which are good absorbers of long wavelength infrared radiations are called greenhouse gases. The main ones are carbon dioxide, water vapour, methane and nitrous oxide. These gases actively contribute in trapping the heat energy within the atmosphere.
Taken together, these naturally occurring greenhouse gases have an average warming effect of nearly \(33\\ ^\\circ\\text{C}\). Because of them, the average temperature at the earth’s surface is about \(15.5\\ ^\\circ\\text{C}\), which is \(60\\ ^\\circ\\text{F}\).
Now imagine removing them. In the absence of greenhouse gases from the atmosphere, the entire heat energy radiated from the earth’s surface and the objects on it would escape out into space. The average temperature on earth would then be \(-18\\ ^\\circ\\text{C}\), or \(0\\ ^\\circ\\text{F}\), instead of \(15.5\\ ^\\circ\\text{C}\).
On the other hand, if there is an increase in the proportion of greenhouse gases in the atmosphere, the average temperature on earth will rise, and it will go above \(15.5\\ ^\\circ\\text{C}\). So the point is not that greenhouse gases are harmful. A right proportion of greenhouse gases is essential for maintaining a comfortable temperature on earth; it is a change in that proportion that causes trouble.
Flowchart
FC 6.4 — The Chain Of The Greenhouse Effect Visible light and short wavelength infrared radiation from the sun pass through the atmosphere → absorbed by clouds, sea water and the earth’s surface → the earth’s surface is heated → the surface radiates long wavelength infrared radiation → the atmosphere is opaque to it, so greenhouse gases and clouds absorb and return it → the earth’s surface and lower atmosphere stay warm
6.7.3 Human Activities That Raise Carbon Dioxide
Measurements over recent decades show that the effective temperature of the earth’s surface has been rising. It has risen by about \(0.08\\ ^\\circ\\text{C}\) (\(0.14\\ ^\\circ\\text{F}\)) per decade since 1880, and the rate of warming since 1982 is more than three times as fast. The global average surface temperature has increased by about \(1\\ ^\\circ\\text{C}\) compared with the pre-industrial era, and the rise is expected to continue by several degrees more if things go on as they are.
The reason is the increase in the proportion of greenhouse gases present in the earth’s atmosphere. Because of that increase, more of the heat radiated from the earth’s surface is trapped within it. It is believed that human activities are responsible, particularly for the rise in carbon dioxide.
Three human activities stand behind that rise.
- The burning of fuels, deforestation, transportation and industrial production, particularly cement factories.
- Increase of population — human activity releases nearly 32 gigatonnes of carbon dioxide each year.
- Imbalance of the carbon dioxide cycle. The oceans do not absorb the full amount of carbon dioxide, and plants are not able to change all of it back into oxygen.
The increase in the concentration of carbon dioxide due to these activities is responsible for about \(60%\) of the increase in the greenhouse effect. Apart from this, rice cultivation, animal husbandry, natural gas exploration, burning of biomass while clearing forests, and leakage from natural gas pipelines have doubled the concentration of methane, which also adds to the greenhouse effect.
Thus the increase in greenhouse gases in the atmosphere enhances the greenhouse effect, and this causes global warming — the subject of the next section.
6.8 Global Warming
The last section ended with a sentence that needs unpacking: a stronger greenhouse effect causes global warming. This section says what that means, what is driving it, and what is expected to follow from it.
Our earth gets heated up by absorbing visible light and short wavelength infrared radiation received from the sun. The greenhouse gases — carbon dioxide, methane and chlorofluorocarbons among them — trap the long wavelength infrared radiation emitted from the earth’s surface, and so keep that surface warm at an average temperature of \(15.5\\ ^\\circ\\text{C}\).
It has been observed that over a fifty-year period in the 20th century, the average temperature of the earth’s atmosphere rose by about \(0.74 \\pm 0.18\\ ^\\circ\\text{C}\). The rate of increase now is much greater than it was then. Fig. 6.8-1 shows the general shape of the change.
Diagram
Fig. 6.8-1 — Rise In The Average Surface Temperature Of The Earth Line graph. X-axis: year, marked at 1880, 1920, 1960, 2000 and 2020. Y-axis: rise in average surface temperature above the pre-industrial value, in °C, marked 0, 0.2, 0.4, 0.6, 0.8, 1.0. Draw a single line that starts near 0 at 1880, rises gently and unevenly to about 0.3 by 1960, and then climbs more and more steeply to about 1.0 at 2020. Draw a straight dashed chord joining the point at 1880 to the point at 1980 and label it ‘average rate over this period’. Draw a second, much steeper dashed chord joining the point at 1982 to the point at 2020 and label it ‘average rate over this period’.
An increase in the average temperature of the earth implies an increase in the amount of greenhouse gases present in its atmosphere, so that they could trap more of the heat radiated from the earth’s surface. It is believed that human activities such as burning of fossil fuels, industrial growth, clearing of forests and the use of automobiles have played a significant role in increasing the greenhouse gases, particularly carbon dioxide.
6.8.1 Causes Of Global Warming
The cause of global warming is the increase in the concentration of greenhouse gases present in the atmosphere of the earth, due to human activities. The three gases that have increased most are set out in Table 6.4.
Thus the increase in greenhouse gases in the atmosphere enhances the greenhouse effect, and hence causes global warming.
Flowchart
FC 6.5 — From Human Activity To Global Warming Burning of fossil fuels, industrial growth, clearing of forests, use of automobiles → concentration of greenhouse gases in the atmosphere increases → more long wavelength infrared radiation from the earth’s surface is absorbed and returned → the greenhouse effect is enhanced → the average effective temperature near the earth’s surface rises → global warming
6.8.2 Impacts Of Global Warming On Life On Earth
The increase in the proportion of greenhouse gases in the atmosphere has already had the following effects on life on earth.
- The variable changes in the climate in different parts of the world have created difficulties, and have forced people and animals to migrate from one place to another.
- The blooming season of different plants has changed.
- The regional climate, which has an immediate effect on simple organisms and plants, has also changed.
- The world’s ecology has changed.
- Deaths due to heat strokes have increased.
6.8.3 Future Predictions
It is not possible to make very accurate predictions of the impact of global warming in the future. Predictions can still be made, though, by looking at the changes in natural phenomena that we are facing now. Nine of them follow.
Living Things And The Oceans
- Dislocation and disappearance of plant and animal species. At the present rate of increase of the greenhouse effect, it is expected that nearly \(30%\) of plant and animal species will vanish by the year 2050, and up to \(70%\) by the end of 2100. This will disrupt the ecosystem. Animals from the equatorial region will shift to higher latitudes in search of ice and cold regions. The absorption of carbon dioxide by the oceans will cause acidification, because of which marine species will migrate.
- Warming of oceans. The temperature of ocean water will increase. Many species in the ocean will either die or disappear, while various other species which prefer warm water will increase greatly in number.
- Melting of glaciers. The frozen tundra in Siberia has started melting, and Greenland has experienced 32 glacial earthquakes in one year. The Arctic snow cover is expected to be ice-free at the end of the melting season within a few decades. The global average sea level has risen at a rate of \(3.1\\ \\text{mm}\) per year, and this rate is expected to increase in future. The amount of oxygen dissolved in the oceans is also expected to decrease, which will have an adverse effect on marine life.
People, Farming And Weather
- Shift in farming regions. In the near future, warming of nearly \(3\\ ^\\circ\\text{C}\) will result in poor yield in farms in low latitude regions, and will increase the risk of malnutrition. Crop yield is expected to increase in middle and high latitude regions, so farmers will have to shift their farming region from low latitudes to high latitudes.
- Increase in new diseases and heat related deaths. Many new diseases will emerge, because bacteria survive better and multiply faster at increased temperatures. Higher humidity and warmer regions will extend the distribution of mosquitoes. Deaths due to heat strokes will also increase.
- Change in regional climate. The warming over land will increase, and will be maximum at high northern latitudes while minimum over the southern latitudes. The frequency of hot extremes, heat waves and heavy precipitation will also increase.
- Variable changes in the climate. These will result in an increase in the number of people suffering deaths, diseases and injuries from floods, storms and droughts.
- Increase in cost of air conditioning. Because of the warming, air conditioning will consume more electric energy, and so will cost more.
- Change in sea level. Due to melting of ice, the area of sea ice around both the poles is shrinking, and a large part of it is expected to be lost. The sea level will therefore rise. Buildings and roads in coastal areas will get flooded, and could suffer damage from hurricanes and tropical storms.
6.9 Ways To Minimise The Impact Of Global Warming
If the cause of global warming is a rise in greenhouse gases, then reducing the impact means holding that rise down. Three main kinds of measure must be taken: technological measures, economic measures and policy measures. They are inter-related, and must be taken at the same time rather than one after the other.
Flowchart
FC 6.6 — The Three Kinds Of Measure Against Global Warming Measures to minimise the impact of global warming → technological measures → renewable sources for electricity, battery-operated vehicles, bio-char stoves Measures to minimise the impact of global warming → economic measures → reforestation and sustainable use of land, carbon tax on industries Measures to minimise the impact of global warming → policy measures → educating children for a sustainable lifestyle, controlling population growth
6.9.1 Technological Measures
Economic growth and population growth both increase the consumption of fuel, and so both are responsible for the release of greenhouse gases. Three technological measures help to check this.
Renewable Sources For Generating Electricity
Fossil fuel-based power plants are the main source of the greenhouse gases generated by human activity. They produce nearly \(21.3%\) of the total greenhouse gases released.
Renewable sources of energy — wind energy, solar energy, tidal energy and geothermal energy — release no such gases while generating electricity. Using them in place of fossil fuel-based power plants is the single largest technological change available, and reducing our dependence on fossil fuel plants is the aim of that change.
Diagram
Fig. 6.9-1 — Renewable Sources Used To Generate Electricity Four panels in a row, each a simple labelled line drawing. Panel 1: a tall wind turbine with three blades on open ground, labelled ‘wind energy’. Panel 2: a row of flat solar photovoltaic panels tilted towards the sun, labelled ‘solar energy’. Panel 3: a coastal barrage across an inlet with a turbine housing set into it and sea waves on one side, labelled ‘tidal energy’. Panel 4: a pipe drawing steam from below the ground surface into a small turbine building, labelled ‘geothermal energy’. Add a common heading above the row: ‘sources that generate electricity without releasing greenhouse gases’.
Battery-Operated Vehicles
Cars, lorries and trucks presently in use for transportation are run by internal combustion engines, which burn fuel and release greenhouse gases. They contribute nearly \(14%\) of the total greenhouse gas emission.
Switching such vehicles to battery-operated ones — electric cars, bikes and scooters — reduces carbon dioxide emission drastically. Two conditions matter, though. The electricity used for charging the battery must itself be generated from renewable sources, or the emission has merely been moved elsewhere. And the vehicles should be used at their full capacity, with the size of the vehicles reduced.
Bio-Char Stoves For Cooking
In many parts of the world, biomass is the main fuel used for cooking, and burning it in the open contributes significantly to the increase of greenhouse gases.
A bio-char stove burns the biomass in the absence of air, inside a specially constructed stove. Burning without air releases smokeless combustible gases — methane and hydrogen — which do the cooking, and leaves behind a residue of charcoal. That charcoal can be buried in the soil, so the carbon in it is locked away instead of going into the atmosphere.
6.9.2 Economic Measures
Industrial growth and deforestation, driven by population growth, have caused the increase in the greenhouse effect. Two economic measures are needed to check them.
Reforestation And Sustainable Use Of Land
In many developing countries, the pressure of population and industrial growth has resulted in unsustainable agricultural practices, which are responsible for about \(90%\) of deforestation.
Such countries must be helped to reforest and to maintain forest habitats. The loss of forest can be verified by satellite imaging, and international agencies can then compensate the countries concerned for protecting the forest rather than clearing it.
Industries To Pay Carbon Tax
Industries emit carbon dioxide to a great extent. A carbon tax is a charge placed on that emission, so that releasing carbon dioxide has a cost attached to it.
The tax can be calculated on the basis of the carbon emission from the industry, the number of employee hours, and the turnover of the industry. It encourages industry to use energy efficient offices, and to avoid the travelling of its employees by holding meetings through tele-conferencing.
6.9.3 Policy Measures
Two policy measures are open to a government.
Educating Children To Live A Sustainable Lifestyle
Children can be taught that a less competitive and more cooperative society is a happier one, and that consuming more and buying more need not be the aim of life. For a sustainable life, we must make full use of what we already have, since materialistic gains give only temporary satisfaction.
Controlling Population Growth
The world population was expected to increase from \(7.1\) billion in the year 2012 to \(9.15\) billion by the year 2050, with most of the growth taking place in developing countries. A larger population consumes more fuel, so its growth adds to the release of greenhouse gases.
Population growth can be moderated through free and easy access to family planning, welfare provisions that support smaller families, and the empowerment of women through education and freedom to choose their career.
An International Agreement
Measures like these work only if many countries take them together. At the 24th United Nations Climate Change Conference, COP24/CMP14, held in Poland from the 3rd to the 14th of December 2018, several nations expressed deep concern at the present rate of increase of greenhouse gases.
They committed to limiting global warming to \(1.5\\ ^\\circ\\text{C}\) compared with pre-industrial levels by the year 2100, for which a goal of zero carbon emission is to be achieved between 2030 and 2050.
6.10 Energy Degradation
In daily life we are constantly transforming energy from one form into the form we happen to need. Electrical energy becomes light in a lamp; chemical energy in fuel becomes the motion of a vehicle.
According to the law of conservation of energy, the energy we start with must be accounted for in full. If that were the end of the story, the given form of energy would get completely converted into the desired useful form, with no loss at all.
6.10.1 Dissipation And The Degraded Form Of Energy
In practice this is not what happens. In transforming energy from one form to the other desired form, the entire energy does not change into the desired form. A part of it changes either into some other undesirable form — usually heat, produced by friction — or is lost to the surroundings by radiation, and is then of no use to us.
This conversion of energy into an undesirable, non-useful form is called the dissipation of energy. Since this part of the energy is no longer available to us for any productive purpose, we call it the degraded form of energy.
Notice carefully what has and has not happened. No energy has been destroyed — the total is exactly what it was. What has changed is how much of that total we can still put to work.
With more and more use of energy, the degraded form of energy will gradually increase, while the energy available for productive purposes will gradually decrease — because the total energy remains constant.
6.10.2 Everyday Examples Of Energy Degradation
Six familiar situations show the same thing happening.
- Lighting a bulb. When we light a bulb using electricity, less than \(25%\) of the electrical energy converts into light energy. The remaining part changes into heat in the filament, and into other invisible radiations. This energy is ultimately imparted to the atmosphere as the vibrational kinetic energy of air molecules, where it is of no use to us.
- Running a vehicle. Only a part of the energy obtained from the fuel is used in running the vehicle. The major part is wasted in heating the moving parts of the machine, in doing work against friction between the ground and the tyres, and in the form of sound.
- Cooking food over a fire. The major part of the heat energy obtained from the fuel is radiated out into the atmosphere instead of entering the food. This radiated energy is of no use to us, and is thus a degraded form of energy.
- Running electrical appliances. When electrical appliances are run by electricity, an appreciable part of the electrical energy is wasted in the form of heat energy.
- Transmitting electricity. In transmission of electricity from a power generating station, a lot of electrical energy is wasted as heat in the line wires that carry it.
- Working of machines. All machines have an efficiency less than 1, that is, less than \(100%\). Efficiency is the fraction of the input energy that appears as useful output, so this means only a fraction of the input energy is used for doing useful work, and the rest goes to the degraded form.
Flowchart
FC 6.7 — Energy Conversions In An Electric Lamp Electrical energy supplied to the lamp → branch 1: light energy, less than 25% of the input, the useful part → leaves the lamp as visible light Electrical energy supplied to the lamp → branch 2: heat in the filament and invisible radiations, more than 75% of the input → imparted to the atmosphere as vibrational kinetic energy of air molecules → degraded energy
Diagram
Fig. 6.10-1 — Useful And Degraded Energy In An Electric Lamp Energy-flow diagram drawn left to right. On the left, a broad horizontal band labelled ‘electrical energy supplied, 100 units’ entering a box labelled ‘filament lamp’. Out of the right of the box, draw one narrow band, about a fifth of the width of the input band, continuing horizontally and labelled ‘light energy, less than 25 units — useful’. Draw a second, much wider band branching downwards from the box, labelled ‘heat and invisible radiation, more than 75 units — degraded’. Show the wide downward band ending in a row of small air molecules labelled ‘energy spread into the atmosphere’. Keep the total width of the two output bands equal to the width of the input band, and add a note beneath: ‘the total is unchanged; the useful share is not’.
From all these examples we reach one conclusion. In every process of transferring available energy into a useful form, a good fraction of it changes into a non-productive or degraded form.
6.11 Summary
- Heat is produced either by doing work or by supplying energy in some other form, such as electrical or chemical energy. Heat is therefore itself a form of energy.
- The molecules of a body are in random motion and attract one another, so they possess kinetic energy and potential energy. The total of these over all the molecules is the internal energy of the body.
- When a hot body is kept in contact with a cold body, energy flows from the hot body to the cold body. Heat is the form of energy that is transferred between two bodies at two different temperatures when kept in contact.
- A body feels hot when heat flows from it into our hand, and cold when heat flows from our hand into it.
- The SI unit of heat is the joule (J) and its CGS unit is the erg. Other units are the calorie (cal) and the kilocalorie (kcal). \[1\\ \\text{J} = 10^{7}\\ \\text{erg},\\qquad 1\\ \\text{kcal} = 1000\\ \\text{cal},\\qquad 1\\ \\text{cal} = 4.186\\ \\text{J}\]
- Temperature is the quantity which indicates the thermal state of a body, that is, its degree of hotness or coldness. It determines the direction of flow of heat when two bodies at different temperatures are placed in contact.
- Two bodies at the same temperature need not contain equal amounts of heat. The heat contained in a body depends on its mass, its temperature and the material of the body.
- The SI unit of temperature is the kelvin (K). Temperature is also measured in degree celsius (\(^\\circ\\text{C}\)) and degree fahrenheit (\(^\\circ\\text{F}\)).
- A degree is the same size on the Celsius and Kelvin scales, so the two are related by \[t\\ \\text{K} = 273 + t\\ ^\\circ\\text{C}\] where the left side is the temperature in kelvin and \(t\) on the right is the same temperature in degree celsius.
- The zero of the Kelvin scale, \(0\\ \\text{K}\), is called absolute zero and lies at \(-273\\ ^\\circ\\text{C}\). No temperature can be lower, so a negative value is not possible on the Kelvin scale.
- The ice point is \(0\\ ^\\circ\\text{C}\), \(32\\ ^\\circ\\text{F}\) and \(273\\ \\text{K}\); the steam point is \(100\\ ^\\circ\\text{C}\), \(212\\ ^\\circ\\text{F}\) and \(373\\ \\text{K}\). Between them there are 100 equal degrees on the Celsius and Kelvin scales but 180 equal divisions on the Fahrenheit scale, so one Celsius degree equals \(\\tfrac{9}{5}\) of a Fahrenheit degree.
- The Celsius and Fahrenheit scales are related by \[\\frac{C}{5} = \\frac{F-32}{9}\] where \(C\) is the temperature in \(^\\circ\\text{C}\) and \(F\) is the same temperature in \(^\\circ\\text{F}\).
- The expansion of a substance on heating is called thermal expansion. In a solid, the increase in length is linear expansion, the increase in area is superficial expansion and the increase in volume is cubical expansion.
- Liquids and gases have no definite shape, so they show only cubical expansion. On heating, liquids expand more than solids, and gases expand much more than liquids.
- A few substances contract on heating over a certain range of temperature: water from \(0\\ ^\\circ\\text{C}\) to \(4\\ ^\\circ\\text{C}\), silver iodide from \(80\\ ^\\circ\\text{C}\) to \(141\\ ^\\circ\\text{C}\), and silica below \(-80\\ ^\\circ\\text{C}\). The expansion of a substance on cooling within such a range is called anomalous expansion.
- The expansion of water when it is cooled from \(4\\ ^\\circ\\text{C}\) to \(0\\ ^\\circ\\text{C}\) is known as the anomalous expansion of water.
- The volume of a fixed mass of water is minimum at \(4\\ ^\\circ\\text{C}\); the volume of \(1\\ \\text{g}\) of water at \(4\\ ^\\circ\\text{C}\) is \(1.0000\\ \\text{cm}^3\).
- The density of water is maximum at \(4\\ ^\\circ\\text{C}\), where it equals \(1\\ \\text{g cm}^{-3}\), that is \(1000\\ \\text{kg m}^{-3}\).
- Hope’s apparatus demonstrates this. A tall metallic cylinder of water is cooled at its middle by a freezing mixture of ice and salt, and thermometers \(T\_1\) near the top and \(T\_2\) near the bottom are read at regular intervals.
- In Hope’s experiment, \(T\_2\) falls first and becomes steady at \(4\\ ^\\circ\\text{C}\), after which \(T\_1\) falls and becomes steady at \(0\\ ^\\circ\\text{C}\), where ice forms at the top. The lower thermometer shows the temperature of maximum density, and the upper one the temperature of water and ice together.
- In a pond in cold weather, water cools and sinks until the whole pond is at \(4\\ ^\\circ\\text{C}\). Water cooled further expands, stays on the surface and freezes there. Ice is a poor conductor of heat, so the water below stays liquid — \(0\\ ^\\circ\\text{C}\) just under the ice and \(4\\ ^\\circ\\text{C}\) at the bottom — and aquatic life survives.
- On very cold nights, water in pipelines expands as it is cooled below \(4\\ ^\\circ\\text{C}\) and bursts the pipes. The capillaries of plants burst for the same reason, and fields are filled with water to protect the crop.
- The earth’s atmosphere is transparent to visible light and short wavelength infrared radiation, which heat the earth’s surface. The surface then radiates long wavelength infrared radiation, to which the atmosphere is opaque.
- The greenhouse effect is the warming of the earth’s surface and its lower atmosphere by the absorption of this long wavelength infrared radiation by greenhouse gases such as carbon dioxide, methane, nitrous oxide, ozone and CFCs.
- The naturally occurring greenhouse gases warm the earth by nearly \(33\\ ^\\circ\\text{C}\), giving an average surface temperature of about \(15.5\\ ^\\circ\\text{C}\). Without them it would be about \(-18\\ ^\\circ\\text{C}\), so a right proportion of these gases is essential.
- Human activities — burning of fuels, deforestation, transportation and industrial production — have increased the proportion of greenhouse gases, particularly carbon dioxide, which accounts for about \(60%\) of the increase in the greenhouse effect.
- Global warming means the increase in the average effective temperature near the earth’s surface due to an increase in the amount of greenhouse gases in its atmosphere.
- Carbon dioxide has increased by up to \(25%\), methane has doubled, and chlorofluorocarbons increase at about \(5%\) per year.
- Global warming has already changed climates, blooming seasons, regional climate and the world’s ecology, and has increased deaths from heat strokes. It is expected to bring loss of species, warming and acidification of oceans, melting of glaciers, rising sea level, shifting farming regions, new diseases and more frequent extremes of weather.
- The impact of global warming can be reduced by technological measures (renewable sources of energy, battery-operated vehicles, bio-char stoves), economic measures (reforestation and sustainable use of land, carbon tax on industries) and policy measures (education for a sustainable lifestyle, control of population growth). These are inter-related and must be taken together.
- Whenever energy is transformed, a part of it changes into an undesirable form — usually heat from friction, or radiation lost to the surroundings. This conversion is called dissipation of energy, and the part so converted is the degraded form of energy.
- The gradual decrease of useful energy due to radiation loss, friction and similar causes is called degradation of energy. The total energy remains constant, but the share available for productive purposes keeps falling.
- Every machine has an efficiency less than \(100%\), so only a fraction of the input energy appears as useful work and the rest is degraded.
Flowchart
FC 6.8 — The Spine Of The Chapter Heat as a form of energy → temperature, which decides the direction of its flow → thermal expansion, the usual effect of heating → anomalous expansion of water between 0 °C and 4 °C → maximum density at 4 °C, shown by Hope’s experiment → ponds freeze from the top and aquatic life survives → heat also travels as radiation → greenhouse gases trap long wavelength infrared radiation from the earth’s surface → an increased proportion of these gases causes global warming → technological, economic and policy measures reduce its impact → in every energy transformation a part is degraded and lost to useful purpose
6.12 Key Terms
- Absolute zero — The zero of the Kelvin scale, \(0\\ \\text{K}\), equal to \(-273\\ ^\\circ\\text{C}\); the lowest temperature possible, at which molecular motion ceases.
- Anomalous expansion — The expansion of a substance on cooling it within a certain range of temperature, instead of the usual contraction.
- Bio-char stove — A stove that burns biomass in the absence of air, giving smokeless combustible gases and leaving charcoal that can be buried in the soil.
- Calorie — An older unit of heat, equal to \(4.186\\ \\text{J}\); symbol cal.
- Carbon tax — A charge placed on an industry according to the carbon dioxide it emits, so that emission carries a cost.
- Convection — The transfer of heat in a fluid by the actual movement of the warmer and cooler parts of the fluid itself.
- Cubical expansion — The increase in the volume of a substance on heating; shown by solids, liquids and gases.
- Degraded form of energy — Energy that has changed into an unwanted form and is no longer available for any productive purpose; measured in joule (J).
- Density — The mass of a substance per unit volume; SI unit kilogram per cubic metre (\(\\text{kg m}^{-3}\)).
- Dissipation of energy — The conversion of a part of the energy being transformed into an undesirable, non-useful form, usually heat from friction or radiation lost to the surroundings.
- Efficiency — The fraction of the input energy of a machine that appears as useful output, usually stated as a percentage; it has no unit and is always less than \(100%\).
- Erg — The CGS unit of heat and of energy, where \(1\\ \\text{J} = 10^{7}\\ \\text{erg}\).
- Global warming — The increase in the average effective temperature near the earth’s surface due to an increase in the amount of greenhouse gases in its atmosphere.
- Greenhouse effect — The warming of the earth’s surface and its lower atmosphere by the absorption of long wavelength infrared radiation, emitted from the surface, by greenhouse gases.
- Greenhouse gases — Gases which are good absorbers of long wavelength infrared radiation, such as carbon dioxide, water vapour, methane and nitrous oxide.
- Heat — The form of energy transferred between two bodies at two different temperatures when they are kept in contact; SI unit joule (J).
- Ice point — The temperature of melting ice: \(0\\ ^\\circ\\text{C}\), \(32\\ ^\\circ\\text{F}\) or \(273\\ \\text{K}\).
- Internal energy — The total kinetic and potential energy of all the molecules of a body; SI unit joule (J).
- Joule — The SI unit of heat and of energy; symbol J.
- Kelvin — The SI unit of temperature; symbol K, written without a degree sign.
- Kilocalorie — A unit of heat equal to \(1000\\ \\text{cal}\); symbol kcal.
- Linear expansion — The increase in the length of a solid on heating.
- Renewable sources of energy — Sources such as wind, solar, tidal and geothermal energy, which nature renews as fast as we use them and which release no greenhouse gases while generating electricity.
- Steam point — The temperature of steam above water boiling at normal atmospheric pressure: \(100\\ ^\\circ\\text{C}\), \(212\\ ^\\circ\\text{F}\) or \(373\\ \\text{K}\).
- Superficial expansion — The increase in the surface area of a solid on heating.
- Temperature — The quantity indicating the thermal state of a body, that is, its degree of hotness or coldness, which determines the direction of flow of heat; SI unit kelvin (K).
- Thermal expansion — The expansion of a substance on heating.
6.13 Points To Ponder
- Suppose water behaved like most substances, growing steadily denser right down to \(0\\ ^\\circ\\text{C}\). Trace what would then happen to a deep lake through a long winter, layer by layer, and to the life in it. Would the lake ever thaw completely in summer?
- Heat always flows from the hotter body to the colder one, and never the other way by itself. Nothing in the law of conservation of energy forbids the reverse. What, then, does the one-way flow of heat tell you that conservation of energy alone does not?
- A block of ice at \(0\\ ^\\circ\\text{C}\) and a bucket of water at \(0\\ ^\\circ\\text{C}\) show the same reading on a thermometer, yet melting the ice needs a great deal more heat. What does this suggest about how far temperature can be trusted as a measure of the energy a body contains?
- The natural greenhouse effect warms the earth by about \(33\\ ^\\circ\\text{C}\), and life depends on it; an increase in the same effect is treated as a danger. Where would you draw the line between the two, and which measured quantity would you use to decide?
- In Hope’s experiment the freezing mixture surrounds the middle of the cylinder. Predict what the two thermometers would record if the same mixture were packed around the top of the cylinder instead, and explain your prediction using density.
- If no machine can ever be \(100%\) efficient, and energy is never destroyed, what exactly is being saved when we speak of ‘saving energy’? Try to state the answer in terms of useful and degraded energy.
6.14 Objective Questions
- The heat energy of a body is the internal energy of its: (1 mark)
- surface
- molecules
- container
- surroundings
- One kilocalorie is equal to: (1 mark)
- \(100\\ \\text{cal}\)
- \(1000\\ \\text{cal}\)
- \(4.186\\ \\text{cal}\)
- \(10^{7}\\ \\text{cal}\)
- The steam point on the Kelvin scale is: (1 mark)
- \(100\\ \\text{K}\)
- \(273\\ \\text{K}\)
- \(373\\ \\text{K}\)
- \(212\\ \\text{K}\)
- Two bodies at the same temperature are placed in contact. The heat that flows from one to the other is: (1 mark)
- zero
- from the heavier to the lighter body
- from the body containing more heat to the other
- from the metal body to the wooden body
- The increase in the surface area of a solid on heating is called: (1 mark)
- linear expansion
- superficial expansion
- cubical expansion
- anomalous expansion
- A fixed mass of water has the least volume at: (1 mark)
- \(0\\ ^\\circ\\text{C}\)
- \(4\\ ^\\circ\\text{C}\)
- \(10\\ ^\\circ\\text{C}\)
- \(100\\ ^\\circ\\text{C}\)
- In Hope’s experiment, the thermometer that finally becomes steady at \(4\\ ^\\circ\\text{C}\) is: (1 mark)
- the upper thermometer \(T\_1\)
- the lower thermometer \(T\_2\)
- both thermometers together
- neither thermometer
- The gases of the atmosphere trap the radiation coming from the earth’s surface because that radiation is: (1 mark)
- visible light
- ultraviolet radiation
- infrared radiation of long wavelength
- X-radiation
- In the absence of greenhouse gases, the average temperature of the earth’s surface would be about: (1 mark)
- \(15.5\\ ^\\circ\\text{C}\)
- \(33\\ ^\\circ\\text{C}\)
- \(0\\ ^\\circ\\text{C}\)
- \(-18\\ ^\\circ\\text{C}\)
- Energy that has changed into a form no longer available for productive work is said to be: (1 mark)
- destroyed
- conserved
- degraded
- created
For each of the following, choose from the codes given below. a. Both A and R are true and R is the correct explanation of A b. Both A and R are true but R is not the correct explanation of A c. A is false but R is true d. A is true but R is false
Assertion (A): A water pipe left full on a very cold night may burst. Reason (R): Water expands when it is cooled from \(4\\ ^\\circ\\text{C}\) to \(0\\ ^\\circ\\text{C}\). (1 mark)
Assertion (A): A negative temperature cannot be recorded on the Kelvin scale. Reason (R): The size of one degree on the Kelvin scale is equal to the size of one degree on the Celsius scale. (1 mark)
Assertion (A): The greenhouse effect is harmful and the earth would be better without it. Reason (R): Greenhouse gases absorb long wavelength infrared radiation emitted from the earth’s surface. (1 mark)
Match each quantity or term in the first list with the correct entry in the second list. (4 marks)
| First list | Second list |
|---|---|
| a. SI unit of heat | i. Ice and salt |
| b. Temperature of maximum density of water | ii. Gradual decrease of useful energy |
| c. Freezing mixture used in Hope’s apparatus | iii. Joule |
| d. Degradation of energy | iv. \(4\\ ^\\circ\\text{C}\) |
- Fill in the blanks.
- One joule is equal to ………… erg. (1 mark)
- On heating, gases expand much more than ………… . (1 mark)
- Ice is a ………… conductor of heat, so it prevents heat escaping from the water of a frozen pond. (1 mark)
- State whether the following statements are true or false.
- Two bodies at the same temperature must contain equal quantities of heat. (1 mark)
- Silver iodide contracts when it is heated from \(80\\ ^\\circ\\text{C}\) to \(141\\ ^\\circ\\text{C}\). (1 mark)
- A machine can be built whose efficiency is greater than \(100%\). (1 mark)
- Name the following.
- The energy that flows from a body at a higher temperature to a body at a lower temperature when the two are kept in contact. (1 mark)
- Any two greenhouse gases other than carbon dioxide. (1 mark)
- The kind of thermal expansion shown by liquids and gases. (1 mark)
- Give one word or phrase for each of the following.
- The expansion of water when it is cooled from \(4\\ ^\\circ\\text{C}\) to \(0\\ ^\\circ\\text{C}\). (1 mark)
- The conversion of a part of the energy being transformed into an unwanted, non-useful form. (1 mark)
- State the SI unit of the following. (3 marks)
- Heat
- temperature
- density.
- Pick the odd one out and give a reason for your choice.
- Wind energy, solar energy, coal, tidal energy. (1 mark)
- Joule, erg, calorie, kelvin. (1 mark)
6.15 Check Your Concepts
Two Marks
Define heat and state its SI unit. (2 marks)
State the relation between the Celsius and the Kelvin scales of temperature, naming each symbol used. (2 marks)
What is meant by the thermal expansion of a substance? Name its three kinds in a solid. (2 marks)
At what temperature is the density of water maximum? State the value of that density in \(\\text{kg m}^{-3}\). (2 marks)
Give a reason: a piece of ice feels cold when it is held in the hand. (2 marks)
Three Marks
Differentiate between heat and temperature, stating three bases of difference. (3 marks)
Why does the temperature of a body rise when it is supplied with heat? State the condition under which this holds. (3 marks)
Explain why a fixed mass of water occupies less space at \(4\\ ^\\circ\\text{C}\) than at either \(0\\ ^\\circ\\text{C}\) or \(8\\ ^\\circ\\text{C}\). (3 marks)
Define the greenhouse effect. Name three greenhouse gases. (3 marks)
What is meant by degradation of energy? Explain with one example from daily life. (3 marks)
Four Marks
Two bodies are placed in contact and no heat flows between them. State what this tells you, and what it does not tell you, about the two bodies. Give a reason. (4 marks)
Explain why the water pipes in a cold town are more likely to burst on a night when the temperature falls below \(0\\ ^\\circ\\text{C}\) than on a mild night. (4 marks)
State the cause of global warming, and describe two of its expected effects on life on earth. (4 marks)
What would happen to the average temperature of the earth’s surface if all the greenhouse gases were removed from the atmosphere? Explain, and state the value it would take. (4 marks)
Name the three main kinds of measure needed to minimise the impact of global warming, and give one example of each. (4 marks)
Five Marks
Describe Hope’s experiment. State the observations of the two thermometers, and explain what the final readings prove about water. (5 marks)
Explain, step by step, how a deep pond in a very cold country freezes, and why fish continue to live in it after the surface has frozen. (5 marks)
‘Energy is always conserved, and yet energy is always being wasted.’ Explain how both statements can be true, using two examples of energy degradation. (5 marks)
6.16 Diagrams, Graphs & Constructions
Draw a labelled diagram of Hope’s apparatus, as in Fig. 6.5-1. Mark the positions of the two thermometers and the freezing mixture, and write against each thermometer the temperature it finally records. (5 marks)
Sketch the graph showing the variation in the volume of \(1\\ \\text{g}\) of water with temperature over the range \(0\\ ^\\circ\\text{C}\) to \(10\\ ^\\circ\\text{C}\), as in Fig. 6.4-1. Label both axes with their units, and mark the temperature at which the volume is least. (4 marks)
Sketch the graph showing the variation in the density of water with temperature over the range \(0\\ ^\\circ\\text{C}\) to \(10\\ ^\\circ\\text{C}\), as in Fig. 6.4-2. State the value of the density at the peak of your curve, with its unit. (4 marks)
Study the temperature–time graphs of Fig. 6.5-2. State which graph belongs to which thermometer, and explain what the flat portion of each graph means physically. (4 marks)
Draw a diagram of an ice-covered pond, as in Fig. 6.6-1, showing the layers of water below the ice. Mark the temperature of the layer just below the ice and of the layer at the bottom. (4 marks)
Draw a labelled diagram to show how the greenhouse effect keeps the earth’s surface warm, as in Fig. 6.7-1. Your diagram must show the radiation coming in from the sun, the radiation leaving the earth’s surface, and the greenhouse gases. (5 marks)
Draw an energy-flow diagram for an electric lamp supplied with 100 units of electrical energy, as in Fig. 6.10-1, showing the useful and the degraded shares. (3 marks)
6.17 Practice With Numericals
Convert \(3\\ \\text{kcal}\) of heat into joule, taking \(1\\ \\text{cal} = 4.186\\ \\text{J}\). (2 marks)
A quantity of heat is \(2.5 \\times 10^{8}\\ \\text{erg}\). Express it in joule. (2 marks)
The temperature of a room is \(45\\ ^\\circ\\text{C}\). Express this temperature on the Kelvin scale. (2 marks)
A beaker contains \(350\\ \\text{g}\) of water at \(4\\ ^\\circ\\text{C}\). Calculate the volume occupied by this water, in \(\\text{cm}^3\). (2 marks)
A heater supplies \(6300\\ \\text{J}\) of heat to a pan of water. Express this heat (i) in calorie and (ii) in kilocalorie, taking \(1\\ \\text{cal} = 4.2\\ \\text{J}\). (3 marks)
The temperature of a body is \(353\\ \\text{K}\). Express this temperature (i) in degree celsius and (ii) in degree fahrenheit. (3 marks)
A lamp is supplied with \(750\\ \\text{J}\) of electrical energy and gives out \(150\\ \\text{J}\) as light energy. Calculate (i) the energy degraded and (ii) the efficiency of the lamp. (3 marks)
The global average sea level rises at about \(3.1\\ \\text{mm}\) per year. Calculate the rise expected over \(20\) years, and express your answer in cm. (3 marks)
A body is cooled from \(77\\ ^\\circ\\text{F}\) to \(41\\ ^\\circ\\text{F}\). Calculate the fall in its temperature in degree celsius. (4 marks)
A country releases \(1.2 \\times 10^{3}\) million tonnes of greenhouse gases in a year, of which fossil fuel-based power plants account for \(21.3%\) and vehicles with internal combustion engines for \(14%\). Calculate the mass released by each of these two sources. (4 marks)