Читать книгу Geochemistry - William M. White - Страница 38

How do you define and measure temperature? We have discussed temperature with respect to the ideal gas law without defining it, though we all have an intuitive sense of what temperature is. We noted above that temperature of a gas is a measure of the average (kinetic) energy of its molecules. Another approach might be to use the ideal gas law to construct a thermometer and define a temperature scale. A convenient thermometer might be one based on the linear relationship between temperature and the volume of an ideal gas. Such a thermometer is illustrated in Figure 2.3. The equation describing the relationship between the volume of the gas in the thermometer and our temperature, τ, is:

(2.19)

where V₀ is the volume at some reference point where τ = 0 (Figure 2.3a) and γ is a scale factor. For example, we might choose τ = 0 to be the freezing point of water and the scale factor such that γ = 100 (Figure 2.3b) occurs at the boiling point of water, as is the case in the centigrade scale. Rearranging, we have:

(2.20)

Then τ = 0 at V = V₀. If V is less than the reference volume, then temperature will be negative on our scale. But notice that while any positive value of temperature is possible on this scale, there is a limit to the range of possible negative values. This is because V can never be negative. The minimum value of temperature on this scale will occur when V is 0. This occurs at:

(2.21)

Thus, implicit in the ideal gas law, which we used to make this thermometer, is the idea that there is an absolute minimum value, or an absolute zero, of temperature, which occurs when the volume of an ideal gas is 0. Notice that while the value (−1/γ) of this absolute zero will depend on how we designed our thermometer (i.e., on V₀), the result, that a minimum value exists, does not. We should also point out that only an ideal gas can have a volume of 0. The molecules of real gases have a finite volume, and such a gas will have a finite volume at absolute zero.

Figure 2.3 An ideal gas thermometer. The colored area is the volume occupied by the ideal gas.

The temperature scale used by convention in thermodynamics is the Kelvin‡ scale. The magnitude of units, called kelvins (not degrees kelvin) and designated K (not °K), on this scale are the same as the centigrade scale, so there are exactly 100 kelvins between the freezing and boiling points of water. There is some slight uncertainty (a very much smaller uncertainty than we need to concern ourselves with) concerning the value of absolute zero (i.e., the value of γ in eqns. 2.20 and 2.21). The scale has been fixed by choosing 273.16 kelvins to be the triple point of water (0.01°C). On this scale, the absolute zero of temperature occurs at 0 ± 0.01 kelvins. The Kelvin scale should be used wherever temperature occurs in a thermodynamic equation.

Temperature has another fundamental property, and this is embodied in the zeroth law of thermodynamics. It is sufficiently obvious from everyday experience that we might overlook it. It concerns thermal equilibrium and may be stated in several ways: two bodies in thermal equilibrium have the same temperature and any two bodies in thermal equilibrium with a third are in equilibrium with each other.