Thermal properties: definition and measurement 247

12.2 Thermal properties: definition and measurement 247

Slope C p

C p = ∆U J/kg.K

∆T Insulated box

T sensor

Energy input per kg (J/kg) Temperature T (K)

Heater

Sample

Figure 12.1 Measuring heat capacity, C p . Its units are J/kg.K.

distortion becoming a problem. The second is the temperature below which the material becomes brittle or otherwise unsafe to use.

It costs energy to heat a material up. The energy to heat 1 kg of a material by

1 K is called the heat capacity or specific heat, and since the measurement is usu- ally made at constant pressure (atmospheric pressure) it is given the symbol C p . Heat is measured in joules 4 , symbol J, so the units of specific heat are J/kg ⭈ K. When dealing with gases, it is more usual to measure the heat capacity at constant volume (symbol C v ) and for gases this differs from C p . For solids the difference is so slight that it can be ignored, and we shall do so here. C p is measured by the technique of

calorimetry, which is also the standard way of measuring the glass temperature T g . Figure 12.1 shows how, in principle, this is done. A measured quantity of energy (here, electrical energy) is pumped into a sample of material of known mass. The temperature rise is measured, allowing the energy/kg.K to be calculated. Real calorimeters are more elaborate than this, but the principle is the same.

Most materials expand when they are heated (Figure 12.2). The thermal strain per degree of temperature change is measured by the linear thermal expansion coefficient, α. It is defined by

where L is a linear dimension of the body. If the material is anisotropic it expands differently in different directions, and two or more coefficients are required. Since strain is dimensionless, the units of α are K ⫺1 or, more conveniently, ‘microstrain/K’, i.e. 10 ⫺6 K ⫺1 .

4 James Joule (1818–1889), English physicist, who, motivated by theological belief, sought to establish the unity of the forces of nature. His demonstration of the equivalence of heat

and mechanical work did much to discredit the caloric theory.

248 Chapter 12 Agitated atoms: materials and heat

mal str Ther

Heater

Sample

Temperature change ∆T (K)

Figure 12.2 Measuring the thermal expansion coefficient, α. Its units are 1/K or, more

usually, 10 ⫺6 /K (microstrain/K).

(W/m q

q W/m 2 q W/m Heat flux 2

Insulation Sample T-gradient (T 1 ⫺ T 2 )/X (K/m)

Figure 12.3 Measuring the thermal conductivity, λ. Its units are W/m ⭈ K.

Power is measured in watts 5 ; 1 watt (W) is 1 joule/second. The rate at which heat is conducted through a solid at steady-state (meaning that the temperature profile does not change with time) is measured by the thermal conductivity, λ (units: W/m.K). Figure 12.3 shows how it is measured: by recording the heat

flux q (W/m 2 ) flowing through the material from a surface at higher temperature

5 James Watt (1736–1819), instrument maker and inventor of the condenser steam engine (the idea came to him whilst ‘walking on a fine Sabbath afternoon’), which he doggedly

developed. Unlike so many of the characters footnoted in this book, Watt, in his final years, was healthy, happy and famous.