Joule Expansion constant internal energy process

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:

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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