Examples of Entropy Change

To make expression (5.5) more understandable, let s consider the freezing of water and melting of ice near 0°C. When one gram of water freezes spontaneously (irreversibly) at 272 K, about 333.5 Joules of heat are liberated q = —333.5 J), or according to (5.5), 

At the equilibrium temperature of 273.15 K no calorimetric measurement is possible, but the equilibrium AS has been determined to within 1% by two measurements of irreversible processes. 

As another example, consider the problem of determining the change in entropy of a substance X between 300 K and 350 K at one bar. We will suppose that the heat capacity of X is constant at exactly 1 J K g so that 50 J are required to heat one gram of X from 300 to 350 K, 25 J to heat it from 300 to 325 K, and so on. It follows that on heating one gram of X from 300 to 350 K in a thermostat (of essentially infinite heat capacity) at 350 K, 

Given enough patience, we could make 50 measurements at one degree intervals, in which case 

Clearly we are approximating an integral, which in a later chapter we will find is 

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