Combining the First and Second Laws

This chapter presents a combination of the First and Second Laws, which leads to a very powerful way of applying thermodynamics to the properties of matter. The fundamental equation is an expression for the change in internal energy that accompanies changes in the volume and entropy of a system. Relations between thermodynamic properties are generated by combining thermodynamic and mathematical expressions for changes in their values. The chapter then considers the Maxwell relations, which are a series of relations between partial derivatives of thermodynamic properties based on criteria for changes in the properties being exact differentials. The Maxwell relations are used to derive the thermodynamic equation of state and to determine how the internal energy of a substance varies with volume. The chapter also looks at the variation of the Gibbs energy of a system, which suggests that it is best regarded as a function of pressure and temperature.