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Internal pressure : ウィキペディア英語版
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 \pi_T. It is defined as a partial derivative of internal energy with respect to volume at constant temperature:
\pi _T = \left ( \frac \right )_T
==Thermodynamic equation of state==
Internal pressure can be expressed in terms of temperature, pressure and their mutual dependence:
\pi_T = T \left ( \frac \right )_V - p
This equation is known as the thermodynamic equation of state for it expresses pressure in terms of thermodynamic properties of the system.
: \right )_V \operatornameS + \left ( \frac \right )_S \operatornameV.
Dividing this equation by \operatorname V at constant temperature gives:
\left ( \frac \right )_T = \left ( \frac \right )_V \left ( \frac \right )_T + \left ( \frac \right )_S
Comparing the above differential with the fundamental thermodynamic equation \operatornameU = T \operatorname S - p \operatorname V
gives
\left ( \frac \right )_V = T and \left ( \frac \right )_S = -p.
This, and the definition of internal pressure, leads to
\pi_T = T \left ( \frac \right )_T - p
One of the Maxwell relations states that
\left ( \frac \right )_T = \left ( \frac \right )_V
Inserting this into the above relation completes the proof.
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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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