One of the simplest yet most significant experiments in the long history of thermodynamics was performed in 1843 by James Joule. The experimental setup consisted of two vessels connected by a valve and immersed in a water bath with a thermometer to detect any temperature changes arising from cooling or heating effects in the two vessels. Initially, one vessel contained air at high pressure and the other was evacuated. When the valve connecting them was opened and the gas expanded to fill both vessels equally (doubled in volume), no increase in the temperature of the water bath was noted. Since the gas in the pair of vessels constitutes a system of constant internal energy1, Joule concluded that the internal energy of the air does not depend on its specific volume. This key feature of ideal gases was stated without proof in Sect. 2.4.1.
Joule's experiment can be modified to more clearly reveal the thermal effects of expansion of a nonideal gas when its internal energy is held constant. Or, how is the partial derivative (dT/dv)u related to the equation of state of the gas? The modification consists of eliminating the water bath, insulating the two vessels against heat flow from outside, and placing the thermometer directly in the first vessel. For simplicity, the valve
1 The water bath serves only to measure the temperature change of the gas following opening of the valve is replaced by a membrane that is ruptured to initiate gas expansion. The apparatus is shown in Fig. 6.2.
To relate the temperature difference between the two states shown in Fig. 6.2 to the equation of state, Eq (6.21b) is divided by dv with u held constant. This yields the desired coefficient:
Was this article helpful?
Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.