When we touch a hot cup of tea or a block of ice, we sense temperature. Temperature is a measure of how hot or cold a body is, and heat is the energy that flows from a hotter body to a colder one. This chapter studies the thermal properties of matter - temperature measurement, thermal expansion, specific heat, latent heat, and the modes of heat transfer.
All matter expands when heated. A metal rail expands on a hot day, a mercury column in a thermometer rises, and the volume of a gas increases with temperature. These changes are described by the coefficients of linear, superficial, and volume expansion. The heat absorbed by a body also raises its temperature by an amount that depends on its specific heat, while a change of state at constant temperature involves latent heat.
Finally, heat is transferred between bodies by conduction, convection, and radiation. Understanding these modes explains why a metal spoon feels hotter than a wooden one, why land and sea breeze blow, and why the Earth receives energy from the Sun across empty space.
Temperature is a measure of the degree of hotness or coldness of a body. Heat is the energy transferred between bodies at different temperatures. When two bodies at different temperatures are brought into thermal contact, heat flows from the hotter body to the colder one until they reach thermal equilibrium. The zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other; this law establishes the concept of temperature and the basis of temperature measurement.
Temperature is measured on different scales. On the Celsius scale, the ice point is 0 degrees C and the steam point is 100 degrees C. The Fahrenheit scale uses 32 and 212 degrees respectively. The Kelvin scale is the absolute scale, with the absolute zero at 0 K and the same size of degree as the Celsius scale. The relation between the scales is:
T(K) = t(C) + 273.15
The relation between Celsius and Fahrenheit is:
F = (9/5) C + 32
Kelvin is the SI unit of temperature.
Most materials expand when heated. The expansion is described by coefficients of expansion. The coefficient of linear expansion, alpha, is the fractional change in length per degree change in temperature:
alpha = delta L / (L * delta T)
so that delta L = L * alpha * delta T. The coefficient of superficial (areal) expansion, beta, describes the change in area, and the coefficient of volume expansion, gamma, describes the change in volume:
delta V = V * gamma * delta T
The three coefficients are related by:
beta = 2 alpha and gamma = 3 alpha
An exception to expansion on heating is water: water contracts when heated from 0 to 4 degrees C and expands thereafter. At 4 degrees C, water has its maximum density. This anomalous behaviour of water is why ice forms at the surface of lakes, protecting aquatic life in winter.
The specific heat capacity of a substance is the amount of heat required to raise the temperature of a unit mass of the substance by one kelvin. If a body of mass m and specific heat c absorbs heat Q and its temperature rises by delta T, then:
Q = m * c * delta T
The SI unit of specific heat capacity is J/kg K. The heat required to raise the temperature of the whole body, m*c, is called its heat capacity, with SI unit J/K. The molar specific heat is the heat required to raise the temperature of one mole of the substance by one kelvin.
Water has a large specific heat of about 4200 J/kg K, which is why coastal regions have moderate climates and why water is used as a coolant in car engines. Metals have small specific heats and heat up and cool down quickly.
When a substance changes state, such as melting or boiling, heat is absorbed or released at constant temperature. The heat absorbed or released per unit mass during a change of state is called latent heat:
L = Q / m
The latent heat of fusion is the heat absorbed when 1 kg of a solid melts into liquid at its melting point without a change of temperature. For ice, the latent heat of fusion is 3.35 x 10^5 J/kg. The latent heat of vaporisation is the heat absorbed when 1 kg of a liquid changes into vapour at its boiling point; for water it is 22.6 x 10^5 J/kg.
Latent heat explains why ice is an effective coolant, why sweating cools the body, and why steam can cause severe burns - it releases a large amount of latent heat when it condenses.
Conduction is the transfer of heat through a material without the bulk motion of the material itself. In solids, heat is conducted by the vibration of atoms and by the free electrons. Metals are good conductors because of their free electrons, while wood, plastic, and air are poor conductors.
The rate of heat conduction through a slab of area A, thickness L, with temperature difference (T1 - T2) between its faces, is given by Fourier's law:
H = k A (T1 - T2) / L
where k is the thermal conductivity of the material, with SI unit W/m K. A material with a high thermal conductivity conducts heat readily. This law explains why a metal spoon in hot tea becomes hot quickly and why woollen clothes keep us warm by trapping air, which is a poor conductor.
Convection is the transfer of heat by the actual movement of the fluid (liquid or gas). When a liquid or gas is heated, it expands, becomes less dense, and rises, while the cooler, denser fluid sinks. This sets up convection currents, which cause land and sea breezes, trade winds, and the circulation of water when heated in a pot.
Radiation is the transfer of heat by electromagnetic waves, which requires no medium. The Sun's heat reaches the Earth through the vacuum of space by radiation. All bodies radiate energy. According to Stefan's law, the rate of emission of energy per unit area by a black body at absolute temperature T is:
E = sigma * T^4
where sigma is the Stefan-Boltzmann constant, 5.67 x 10^-8 W/m^2 K^4. A black body is an ideal body that absorbs all radiation incident on it. Newton's law of cooling states that the rate of loss of heat of a body is proportional to the difference between its temperature and the surroundings' temperature.
| Quantity | Formula | SI Unit |
|---|---|---|
| Heat absorbed | Q = m c delta T | J |
| Linear expansion | delta L = L alpha delta T | m |
| Volume expansion | delta V = V gamma delta T | m^3 |
| Latent heat | L = Q / m | J/kg |
| Conduction rate | H = k A (T1 - T2) / L | W |
| Stefan's law | E = sigma T^4 | W/m^2 |
| Substance | Latent Heat |
|---|---|
| Fusion of ice | 3.35 x 10^5 J/kg |
| Vaporisation of water | 22.6 x 10^5 J/kg |
| Specific heat of water | 4200 J/kg K |
In this chapter we studied the thermal properties of matter. Temperature scales are connected by T(K) = t(C) + 273.15, and heat is measured through Q = m c delta T using specific heat capacity. Solids expand on heating, with linear and volume expansion coefficients related by gamma = 3 alpha, and water shows the unusual behaviour of maximum density at 4 degrees C. Change of state at constant temperature is governed by latent heat, which is large for water and explains many cooling applications. Heat is transferred by conduction, governed by Fourier's law H = kA(T1 - T2)/L, by convection through fluid currents, and by radiation, described by Stefan's law E = sigma T^4. These concepts lead directly into thermodynamics, where we study the conversion of heat into work.