Elementary Applications of the First Law

The first law of thermodynamics leads to many simple and useful conclusions. It leads to a relation between the molar heat capacities, Cp, at constant pressure, and Cy, at constant volume (Fig. 2.5 and Table 2.1). Consider a one-component substance with fixed mole number N — Then, using (2.2.3) and (2.2.6), since the energy is a function of the volume and temperature, the change in the energy dU can be written as 

From this it follows that the heat supplied can be written as 

If the system is heated at a constant volume, since no work is done, the change in the energy of the system is entirely due to the heat supplied. Therefore 

On the other hand, if the system is heated at constant pressure, we have from (2.3.2) that 

The right-hand side of (2.3.5) is equal to the additional amount of heat required in a constant-pressure, or isobaric, process to compensate for the energy expended due to expansion of volume. 

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