Internal pressure

Internal pressure is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature. It has the same dimensions as pressure, the SI unit of which is the pascal.

Internal pressure is usually given the symbol ${\displaystyle \pi _{T}}$. It is defined as a partial derivative of internal energy with respect to volume at constant temperature:

${\displaystyle \pi _{T}=\left({\frac {\partial U}{\partial V}}\right)_{T}}$

Internal pressure can be expressed in terms of temperature, pressure and their mutual dependence:

${\displaystyle \pi _{T}=T\left({\frac {\partial p}{\partial T}}\right)_{V}-p}$

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