
6 The Principles of Thermodynamics
Example 1.1: Comparing thermometers
Consider two constant volume thermometers, one of which is based on an ideal gas,
and the other on a substance whose pressure at fixed volume follows the law P(T )=
aT + bT
2
, T being the absolute scale. Find expressions for the two temperatures T
1
and T
2
in terms of T. Show that the temperature(on the absolute scale) at which the
discrepancy between the scales is maximal is always the mid-point between the fiducial
temperatures.
Let us take the ideal gas law to be P = cT , where c depends on the molar
fraction of the ideal gas used in the thermometer and its volume. Let the
fiducial