- #1
arpon
- 235
- 16
We know,
$$dU=TdS-PdV$$
##\int PdV## can be calculated if the equation of state is given.
I tried to express ##S## as a function of ##P ,V## or ##T## (any two of those).
$$dS=\left(\frac{\partial S}{\partial V}\right)_T dV+\left(\frac{\partial S}{\partial T}\right)_V dT$$
$$=\left(\frac{\partial P}{\partial T}\right)_V dV+\left(\frac{\partial S}{\partial P}\right)_V \left(\frac{\partial P}{\partial T}\right)_V dT~~~ [Using ~~Maxwell's~~ relation]$$
$$=\left(\frac{\partial P}{\partial T}\right)_V dV-\left(\frac{\partial V}{\partial T}\right)_S \left(\frac{\partial P}{\partial T}\right)_V dT~~~[Using ~~Maxwell's~ ~relation]$$
All the terms except ##\left(\frac{\partial V}{\partial T}\right)_S## can be calculated using the equation of state.
Any suggestion will be appreciated.
$$dU=TdS-PdV$$
##\int PdV## can be calculated if the equation of state is given.
I tried to express ##S## as a function of ##P ,V## or ##T## (any two of those).
$$dS=\left(\frac{\partial S}{\partial V}\right)_T dV+\left(\frac{\partial S}{\partial T}\right)_V dT$$
$$=\left(\frac{\partial P}{\partial T}\right)_V dV+\left(\frac{\partial S}{\partial P}\right)_V \left(\frac{\partial P}{\partial T}\right)_V dT~~~ [Using ~~Maxwell's~~ relation]$$
$$=\left(\frac{\partial P}{\partial T}\right)_V dV-\left(\frac{\partial V}{\partial T}\right)_S \left(\frac{\partial P}{\partial T}\right)_V dT~~~[Using ~~Maxwell's~ ~relation]$$
All the terms except ##\left(\frac{\partial V}{\partial T}\right)_S## can be calculated using the equation of state.
Any suggestion will be appreciated.