Heat and Temperature

In everyday language we often use the words "heat" and "temperature" as if they mean the same thing, but in science they are quite different. Heat is a form of energy that flows from a hotter object to a colder one. It is the total energy of all the moving particles in an object. Temperature, on the other hand, is a measure of how hot or cold an object is — it tells us the degree of hotness, not the total energy. Heat is energy in transit; temperature is a number that tells us the hotness.

A key idea is that heat always flows from a body at higher temperature to a body at lower temperature, never the other way by itself. When a hot cup of tea is left in a room, heat flows from the hot tea to the cooler surroundings until both reach the same temperature. The flow of heat stops when the two objects reach the same temperature (called thermal equilibrium). So temperature decides the direction in which heat flows.

Heat and temperature have different SI units. The SI unit of heat is the joule (J), since heat is a form of energy (energy is measured in joules). The SI unit of temperature is the kelvin (K), though in everyday life we usually measure temperature in degrees Celsius (°C). So we say a cup of tea contains a certain amount of heat energy (in joules) and is at a certain temperature (in degrees Celsius or kelvin).

An important point is that temperature does not depend on the amount of substance, but heat does. For example, a small cup of boiling water and a large bucket of boiling water are at the same temperature (100 °C), but the large bucket contains much more heat energy, because it has many more hot particles. This is why the bucket can warm a room more than the cup, even though both are equally hot. Understanding that heat is energy and temperature is the degree of hotness, and that they have different units, is the foundation for studying thermometers, heat transfer, and the effects of heat in this chapter.

To measure temperature accurately, we use an instrument called a thermometer. Most common thermometers work on a simple principle: most substances expand when heated and contract when cooled. A thermometer usually contains a liquid (such as mercury or coloured alcohol) in a thin tube; when the temperature rises, the liquid expands and rises up the tube, and when it falls, the liquid contracts and goes down. The level of the liquid against a marked scale tells us the temperature.

There are different kinds of thermometers for different uses. A clinical thermometer is used to measure the temperature of the human body. It has a narrow range (because body temperature stays within narrow limits, around 37 °C) and a small "kink" (constriction) in the tube that stops the liquid from flowing back, so the reading can be taken after the thermometer is removed. A laboratory thermometer is used in science labs to measure a wider range of temperatures (for example, the temperature of liquids being heated); it has a longer scale and no kink. Modern digital thermometers display the temperature as a number on a screen.

Temperature is measured on different scales. The Celsius scale (°C) is the most commonly used everyday scale; on it, the freezing point of water is 0 °C and the boiling point of water is 100 °C (at normal pressure). The Fahrenheit scale (°F) is used in some countries; on it, water freezes at 32 °F and boils at 212 °F. The Kelvin scale (K) is the SI scale used in science; it starts from the lowest possible temperature, called absolute zero (0 K), and on it water freezes at 273 K and boils at 373 K. A change of 1 °C equals a change of 1 K.

These three scales — Celsius, Fahrenheit, and Kelvin — are simply different ways of numbering the same temperatures, much like measuring length in different units. Because they are related in fixed ways, a temperature given on one scale can be converted to another using conversion formulas (which we study in the next topic). Understanding thermometers — how they use expansion, the types for body and lab use, and the Celsius, Fahrenheit, and Kelvin scales — lets us measure and compare temperatures precisely.

Since temperature can be measured on the Celsius (°C), Fahrenheit (°F), and Kelvin (K) scales, we often need to convert a temperature from one scale to another. This is just like converting between units of length. The three scales are related by fixed formulas, because they are different ways of numbering the same temperatures. Knowing the conversions lets us understand a temperature given on any scale.

The relationship between the three scales can be written as a single combined formula: C / 5 = (F − 32) / 9 = (K − 273) / 5 Here C is the Celsius temperature, F is the Fahrenheit temperature, and K is the Kelvin temperature. From this combined relation, we can pick out the formula we need for any particular conversion. The numbers 5, 9, 32, and 273 come from the fixed points (freezing and boiling of water) on each scale.

To convert between Celsius and Fahrenheit, we use C/5 = (F − 32)/9. From this, to go from Celsius to Fahrenheit: F = (9/5) × C + 32, and to go from Fahrenheit to Celsius: C = (5/9) × (F − 32). For example, to convert 100 °C to Fahrenheit: F = (9/5) × 100 + 32 = 180 + 32 = 212 °F — which is correct, since water boils at both 100 °C and 212 °F.

To convert between Celsius and Kelvin, the relation is simpler because the scales differ only by a shift of 273 (their degrees are the same size): K = C + 273 and C = K − 273. For example, 0 °C = 0 + 273 = 273 K (freezing point of water), and 27 °C = 27 + 273 = 300 K. Using these formulas — C/5 = (F − 32)/9 = (K − 273)/5 — we can change any temperature from one scale to another, allowing us to compare and understand temperatures measured on different scales.

Heat, being a form of energy, can travel (transfer) from one place to another. There are three ways in which heat is transferred: conduction, convection, and radiation. Each works differently and is important in different situations. Understanding these three modes explains how a metal spoon gets hot in tea, how a room warms up, and how heat from the Sun reaches the Earth across empty space.

Conduction is the transfer of heat through a solid without the substance itself moving. When one end of a solid is heated, the particles there vibrate faster and pass their energy to neighbouring particles, so heat travels through the material from the hot end to the cold end. Metals are good conductors of heat (which is why a metal spoon in hot tea soon becomes hot to hold), while wood, plastic, and air are poor conductors (insulators). Conduction is the main way heat moves through solids.

Convection is the transfer of heat in liquids and gases (fluids) by the actual movement of the heated fluid. When a fluid is heated, the warm part becomes less dense and rises, while cooler, denser fluid sinks to take its place; this sets up circulating convection currents that carry heat throughout the fluid. Convection explains how water heats up in a pan, how a room is warmed by a heater, and how sea breezes and winds form. It cannot occur in solids, because their particles cannot move freely.

Radiation is the transfer of heat without any medium, by means of invisible heat rays (a kind of energy wave). Radiation is the only way heat can travel through a vacuum (empty space). This is how heat from the Sun reaches the Earth across the empty space, and how we feel the warmth of a fire or a hot object without touching it. Dark, dull surfaces absorb and emit radiation well, while shiny, light surfaces reflect it. So heat travels by conduction (through solids), convection (through moving fluids), and radiation (through space without a medium) — three modes that together explain the movement of heat all around us.

When substances are heated, several important effects occur. The first is thermal expansion: most substances expand (increase in size) when heated and contract (decrease in size) when cooled. This happens because heating makes the particles vibrate more and move slightly farther apart. Solids, liquids, and gases all expand on heating, with gases expanding the most and solids the least. Thermal expansion has many practical effects: gaps are left between railway tracks and in bridges to allow for expansion in hot weather, and electric and telephone wires are left slightly loose so they do not snap when they contract in winter.

A useful application of the expansion of solids is the bimetallic strip. This is made of two different metals joined together, which expand by different amounts when heated. As a result, the strip bends when its temperature changes. This bending is used in thermostats — devices that switch heating or cooling appliances on and off automatically to control temperature — and in fire alarms. So the simple fact that metals expand differently is put to clever use.

The second effect involves how much heat different substances need to warm up, described by specific heat capacity. Specific heat capacity is the amount of heat needed to raise the temperature of 1 kilogram of a substance by 1 degree. Different substances have different specific heats — water has a very high specific heat, meaning it needs a lot of heat to warm up and releases a lot when it cools. The heat required is given by Q = m c ΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature change. The high specific heat of water explains why it is used as a coolant, and why sea breezes occur (land heats and cools faster than the sea).

The third effect is latent heat, the heat involved in changing the state of a substance (melting or boiling) without changing its temperature. When ice melts into water, or water boils into steam, heat is absorbed but the temperature stays the same during the change — this absorbed heat is the latent heat. The heat needed to melt a solid into a liquid is the latent heat of fusion, and the heat needed to change a liquid into a gas is the latent heat of vaporisation. Latent heat plays a big role in climate (for example, when water evaporates and condenses) and in why steam burns are so severe. So thermal expansion, specific heat, and latent heat together describe the rich variety of effects that heat produces, completing our study of heat and temperature.