# 10: Some Mathematical Consequences of the Fundamental Equation

- Page ID
- 151724

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- 10.3: Expressing Thermodynamic Functions with Other Independent Variables
- Evidently, we should be able to express any thermodynamic function using various pairs of state functions. We can do this by transforming the equations that we have already derived. We are particularly interested in P , V , and T as independent variables, because these quantities are readily measured for most systems. In the sections below, we find exact differentials for dS , dE , dH , dA , and dG with V and T and with P and T as the independent variables.

- 10.5: Expressing Thermodynamic Functions with Independent Variables P and T
- We can follow a parallel development to express these thermodynamic functions with P and T as the independent variables.

- 10.14: The Joule-Thomson Effect
- The Joule-Thomson experiment is done by allowing gas from a pressure vessel to pass through an insulated tube containing a throttling valve or a porous plug through which gas flows slowly enough so that the gas upstream from the plug is at a uniform pressure P1, and the gas downstream is at a uniform pressure P2. Depending on the initial temperature and pressure, the pressure drop, and the gas, the temperature of the gas can either decrease or increase as it passes through the plug.