Enthalpy derivative via volume derivative¶

Isothermal derivative of enthalpy w.r.t. pressure can be found using volume as a function of temperature and pressure.

Conditions:

Works for an infinitesimal quasi-static isothermal process.

Links:

Wikipedia, see third table.

temperature¶: temperature of the system.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

pressure¶: pressure inside the system.

Symbol:: p
Latex:: \(p\)
Dimension:: pressure

enthalpy¶: enthalpy of the system.

Symbol:: H(T, p)
Latex:: \(H{\left(T,p \right)}\)
Dimension:: energy

volume¶: volume of the system.

Symbol:: V(T, p)
Latex:: \(V{\left(T,p \right)}\)
Dimension:: volume

law¶

Derivative(H(T, p), p) = V(T, p) - T * Derivative(V(T, p), T)

Latex:: \[\frac{\partial}{\partial p} H{\left(T,p \right)} = V{\left(T,p \right)} - T \frac{\partial}{\partial T} V{\left(T,p \right)}\]