Temperature as Thermal Tension

The effect of different entropy capacities of various substances can be illustrated by Experiment 3.8. 

The entropy capacity depends not only— like the entropy— upon temperature and pressure, but also upon the conditions under which the substance is heated. A substance wDl absorb more entropy when it is allowed to expand freely than it would if its expansion were hindered. Depending on whether in most cases the pressure or more rarely the volume remains constant during the temperature increase, a different change of entropy content and therefore also a different entropy capacity can be observed. One characterizes the two different coefficients, if necessary, by indices Cp and Cy, respectively. If there is no index we always refer to Cp. 

An image developed aheady in the eighteenth cenmry seems especially simple. It imagines temperature as a kind of pressure or tension weighing upon entropy. However, at that time the word entropy was not used. One imagined a fluid like entity that warms a body, and considered it a kind of weightless substance comparable to 

The first equation follows directly from the equation defining the absolute temperature if it is solved for dW. With help from the law of conservation of energy, the second equation follows easily from the first one. This law states that the same effect, no matter how it comes about, always requires the same energy. Whether a certain amount of entropy is generated in a body or added to it, the effect upon the body is identical. It expands, melts, vaporizes, or decomposes in the same manner. It must follow, then, that the energy needed for these processes must be the same. 

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