Thermodynamic Quantities in Reversible Expansions

Isothermal. The procedure used to calculate the work and energy quantities in an isothermal reversible expansion of a real gas is similar to that used for the ideal gas. 

The change in energy in an isothermal expansion cannot be expressed in a simple form without introducing the second law of thermodynamics. Nevertheless, we will anticipate this second basic postulate and use one of the deductions obtainable from it  

For a gas that obeys the van der Waals equation. Equation (5.76) reduces to 

From the first law of thermodynamics, we now can calculate the heat absorbed in the isothermal reversible expansion  

The PVra product can be calculated from the van der Waals equation in the form 

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