Heat

You have probably heard all of these at home. Each has a scientific reason. Try to explain each one before you open the answer.

All four have something in common: they are about heat, about how it moves, and about what it does to things. Let’s start with what heat is.

All matter is made of atoms or molecules, and they are always moving: vibrating, spinning, rushing about. Because they move, they have kinetic energy. The molecules in lukewarm water move faster than those in cold water, and those in hot water move faster still.

Thermal energy is the total kinetic energy of all the molecules of a substance. Take equal masses of hot, tap and cold water: the hot water has the most thermal energy, and the cold water the least.

Not every molecule moves at the same speed; at any moment some are fast and some slow. So we talk about their average kinetic energy. Temperature is a measure of the average kinetic energy of the molecules of a substance. Hotter means the molecules are moving faster, on average.

The SI unit of temperature is the kelvin (K), though in daily life we use the degree Celsius (°C). Temperature is measured with a thermometer. A step of one kelvin is the same size as a step of one degree Celsius; only the starting point is different:

$$T\ (\text{in K}) = t\ (\text{in °C}) + 273$$

More thermal energy, but a lower temperature

Here’s a puzzle. A pan of boiling water is at 100 °C. A big bucket of lukewarm bath water is at 30 °C. Which has more thermal energy?

The molecules in the pan move faster, on average, so the pan has the higher temperature. But the bucket has far more molecules. Each moves more slowly, but there are so many of them that their total kinetic energy is bigger. So the lukewarm bucket has more thermal energy than the boiling pan. The thermal energy of a substance depends on its mass (how many molecules) and on the average speed of its molecules (its temperature).

Heat

Pour the pan of boiling water into the bucket. The fast molecules from the pan bump into the slower ones in the bucket and pass on some of their energy. Thermal energy moves from the hotter water to the cooler water.

The thermal energy that flows from one place to another because of a difference in temperature is called heat. Like every kind of energy, heat is measured in joules (J). It can be measured with an instrument called a calorimeter.

Heat travels in three ways: conduction (through a solid, from molecule to molecule, like the steel plate), convection (carried by a moving liquid or gas, like the hot water rising in a pot), and radiation (as invisible infrared rays, like the warmth you feel from the sun or a fire).

When you touch something and heat flows into your body from it, it feels hot. When heat flows out of your body into it, it feels cold.

Heat always flows from the object at the higher temperature to the object at the lower temperature, never the other way round by itself, until both reach the same temperature. Then the flow stops. This state is called thermal equilibrium.

In a solid, the particles are held close together in a fixed pattern by the forces of attraction between them. They don’t stay still: they vibrate about their places. In a liquid, they are still close but can slide past one another. In a gas, they are far apart and fly about freely (Figure 9.2).

When a solid is heated, its particles gain energy and vibrate harder. As they vibrate more and more, they push one another a little farther apart, and the force of attraction between them gets weaker. So the solid gets a little bigger: its volume increases. It expands. When it gives out heat, its particles slow down, the temperature falls, and the solid contracts. Most substances expand when heated and contract when cooled.

Engineers have to allow for expansion everywhere. Railway tracks and long bridges have small gaps so that they can grow on hot days without buckling; electric and telephone wires are hung a little loose so they don’t snap when they contract in winter. And you can use expansion yourself: if the metal lid of a glass jar is stuck, hold the lid under hot water. The metal expands more than the glass, and the lid comes loose.

Almost every substance expands when it is heated. Water does too, except in one small range of temperature, and that one exception matters enormously.

• When water is heated from 0 °C to 4 °C, it contracts: its volume decreases.
• Above 4 °C, it expands on heating, like everything else.
• Going the other way: water cooled down to 4 °C contracts, but cooled from 4 °C to 0 °C it expands.

So water has its smallest volume and its greatest density at 4 °C (more exactly, 3.98 °C). This unusual behavior is called the anomalous expansion of water (anomalous means “not following the usual rule”).

On top of that, when water at 0 °C freezes, it expands again by about 9%. Ice (density about 917 kg/m³) is less dense than water (1000 kg/m³), and that is why ice floats.

Effects of the anomalous expansion of water

Lakes freeze from the top, and fish survive

In winter, in cold places such as Nepal’s high mountains, the air gets colder than 0 °C. The water at the surface of a lake cools first.

1. While the water is above 4 °C, the cooled surface water becomes denser and sinks, and warmer water rises to take its place. The whole lake cools this way, until all of it is at 4 °C.
2. Now the surface water cools below 4 °C. It becomes less dense, so it stays on top. The heaviest water, at 4 °C, stays at the bottom.
3. Layers form: from the bottom up, water at 4 °C, 3 °C, 2 °C, 1 °C and 0 °C. The top layer freezes into ice, which floats.
4. The ice is a poor conductor of heat, so it works like a blanket: the water below it stays liquid, at about 4 °C at the bottom.

So the lake freezes from the top down, and fish, frogs and water plants live through the winter in the water under the ice.

Burst pipes and cracked bottles

In very cold places, water pipes burst in winter. As the water inside cools below 4 °C, it expands; when it freezes, it expands by about 9% more, and pushes on the pipe with an enormous pressure, far more than the pipe can bear. The same thing cracks a bottle full of water left in the freezer. People in cold places wrap their water pipes, bury them deep, or let the water run slowly through cold nights.

Put these pairs in the hot sun for 15–20 minutes: a steel plate and a ceramic plate; a plastic chair and a wooden chair; a tray of dry sand and a tray of wet soil; a steel vessel and a glass vessel. Then touch them. In each pair, one gets much hotter than the other. Different substances heat up at different rates, even in the same sunshine.

The amount of heat a thing takes in, and how much its temperature rises, depend on what it’s made of, on how much of it there is, and even on its shape and color (a dark, wide object takes in more sunlight).

What decides the heat needed

So the heat $Q$ taken in (or given out) by a substance is:

• directly proportional to its mass $m$, for the same change of temperature: $Q \propto m$ … (i)
• directly proportional to its change in temperature $(T_2 - T_1)$, for the same mass: $Q \propto (T_2 - T_1)$ … (ii)

Combining (i) and (ii): $Q \propto m(T_2 - T_1)$, and so

$$Q = ms(T_2 - T_1) \quad \text{… (iii)}$$

where $s$ is a constant for each substance, called its specific heat capacity. This is the heat equation: the heat taken in or given out by a substance equals its mass × its specific heat capacity × its change in temperature. ($T_1$ is the starting temperature and $T_2$ the final one. Some books write $\Delta T$ or $\theta$ for the change, and $c$ instead of $s$.)

From (iii), $s = \dfrac{Q}{m(T_2 - T_1)}$. Put $m$ = 1 kg and $T_2 - T_1$ = 1 °C, and $s = Q$. So:

The specific heat capacity of a substance is the amount of heat needed to raise the temperature of 1 kg of it by 1 °C.

Its SI unit is the joule per kilogram per degree Celsius (J/kg °C), which is the same as J/kg K, because a step of 1 °C is a step of 1 K.

Substance	Specific heat capacity (J/kg °C)	Substance	Specific heat capacity (J/kg °C)
water	4,200	aluminium	884
ethyl alcohol	2,400	iron	460
kerosene oil	2,010	copper	385
ice	2,100	silver	236
mercury	126	gold	130

So it takes 4,200 J to warm 1 kg of water by 1 °C, but only 2,100 J for 1 kg of ice, and just 130 J for 1 kg of gold. Water and ice are the same substance in two states, yet their specific heat capacities are different. Water’s is one of the highest of any common substance: water is very “hard to heat”, and just as slow to cool.

Calculating heat

Mixing hot and cold: heat lost = heat gained

When hot water is mixed with cold water, heat flows from the hot water to the cold water until they reach the same final temperature. If no heat escapes to the surroundings, all the heat given out by the hot water is taken in by the cold water:

$$\text{heat lost by the hot water} = \text{heat gained by the cold water}$$

This is called the principle of calorimetry (or the principle of mixtures).

Uses of specific heat capacity

Water’s specific heat capacity is very high: every kilogram of water must take in or give out 4,200 J to change its temperature by just 1 °C. That makes it useful in many ways.

• Cooling engines. The radiator of a car, bus or motorbike is full of water (with a little antifreeze). The water flows around the hot engine, takes in a large amount of heat without getting too hot itself, and gives it off to the air in the radiator. Thermal power stations use huge amounts of water for cooling for the same reason.
• Keeping warm. A hot water bag (bottle) filled with hot water gives out a lot of heat while cooling only slowly, so it stays warm for hours. It is used to warm a bed and to ease muscle pain (a hot compress).
• A wet cloth on the forehead helps bring down a high fever. The water takes in a lot of heat from the skin as it warms, and even more as it evaporates.
• Our bodies are mostly water: about 60% of an adult’s mass, more in a baby, and in some animals (a jellyfish) over 90%. All that water absorbs the heat our muscles make without our temperature shooting up, and helps keep us steady at about 37 °C.

Sea breeze and land breeze

On a sunny day the sun warms the land and the sea equally. But dry sand has a specific heat capacity of about 800 J/kg °C, roughly five times less than water’s. So the land heats up much faster than the sea. The air over the hot land becomes warm, expands, gets lighter, and rises, leaving low pressure behind. Cooler air from over the sea flows in to take its place. This cool wind from the sea in the daytime is the sea breeze.

At night, both lose heat by radiation. The land cools quickly; the sea, with its high specific heat capacity, stays warm. Now the warmer air over the sea rises, and cooler air flows from the land out to sea: the land breeze.

These breezes, and the sea itself, which warms and cools so slowly, keep places by the sea from getting very hot by day or very cold at night. In a desert, where there is little water in the sand or the air, the ground heats fast in the day and loses its heat fast at night: deserts can be 45 °C by day and near freezing by night.

Our skin can be fooled (remember the three bowls), so we use thermometers. Each kind uses some property that changes with temperature.

a. Liquid-in-glass thermometer

It has a thin glass bulb filled with a liquid (mercury or colored alcohol), joined to a very fine tube, the capillary tube, with a scale beside it. When the bulb touches a hot object, heat flows into the liquid, the liquid expands, and it rises up the narrow tube. Where it stops on the scale is the temperature. Because the tube is so fine, a tiny expansion makes the thread move a long way, so it is easy to read.

Mercury is a good choice: it conducts heat well (so it responds quickly), it expands evenly, it is shiny and easy to see, it doesn’t stick to glass, and it stays liquid from −39 °C to 357 °C. In very cold places, alcohol thermometers are used instead, because alcohol freezes only at −114 °C. Mercury is poisonous, so under an international treaty, the Minamata Convention, mercury thermometers have been phased out since 2020 in many countries in favor of digital ones.

A clinical thermometer (for measuring body temperature) has a tiny bend, a kink, in its tube just above the bulb. When you take it out of your mouth, the mercury thread breaks at the kink and stays in place, so the doctor can read your temperature. It must be shaken down before it is used again.

b. Digital thermometer

A digital thermometer has a tiny thermistor at its tip: a resistor whose electrical resistance changes a lot with temperature. When the tip touches your body, heat flows into it, its resistance changes, so the current in the circuit changes, and a small chip turns that change into a temperature shown as numbers on the display.

c. Radiation (infrared) thermometer

Every warm object gives out invisible infrared radiation; the hotter it is, the more. A radiation thermometer (infrared thermometer) has a lens that focuses the infrared coming from an object onto a sensor, which turns it into an electrical signal and shows the temperature. It needs no contact: you just point it at the forehead or at a hot pan. That makes it quick, safe and hygienic, which is why it was used everywhere at doorways during the COVID-19 pandemic.

Calibrating a thermometer

Calibration means marking the scale on a thermometer. First, two fixed points are marked:

• the lower fixed point: the temperature of pure melting ice, 0 °C;
• the upper fixed point: the temperature of the steam just above pure water boiling at one atmosphere of pressure (standard sea-level pressure), 100 °C.

The distance between the two is then divided into equal parts. On the Celsius scale it is divided into 100 parts, each 1 °C.

Different scales use different numbers for the same fixed points:

Scale	Lower fixed point (ice melts)	Upper fixed point (water boils)	Parts between them
Celsius	0 °C	100 °C	100
Fahrenheit	32 °F	212 °F	180
Kelvin	273 K	373 K	100

Since each scale spreads the same interval over its own number of parts, you can convert between them:

$$\frac{C - 0}{100} = \frac{F - 32}{180} = \frac{K - 273}{100}$$

Water boils at 100 °C only at sea-level pressure. A liquid boils when its molecules move fast enough to push bubbles of vapor open against the pressure of the air above. If the air pressure is lower, the bubbles form more easily, and water boils at a lower temperature.

The higher you go, the thinner the air and the lower its pressure, so the lower the boiling point. In Kathmandu and Bhaktapur (about 1,400 m) water boils at about 95 °C; at Namche Bazaar (3,440 m) at about 89 °C; and on the summit of Everest at only about 70 °C, not hot enough to cook rice or dal properly. That is why a pressure cooker is so useful in the hills: it traps the steam, raising the pressure inside to about twice that of the air, so the water boils at about 120 °C and food cooks fast.

1. Choose the correct option

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