 #1
Like Tony Stark
 179
 6
 Homework Statement:
 The fundamental equation of a gas is ##A=aVT^{\frac{5}{2}} e^{\frac{\mu}{RT}}##. Determine ##\alpha##, ##\kappa_T## and ##c_P##, and then find the fundamental equation in energetic representation: ##U(S; V; N)##.
 Relevant Equations:

##U##: internal energy; ##T##: temperature; ##\mu##: chemical potential; ##R##: ideal gas constant; ##V##: volume; ##N##: number of moles; ##\alpha##: coefficient of thermal expansion; ##c_P##: heat capacity at constant pressure; ##\kappa_T##: compressibility at constant temperature.
##\alpha=\frac{1}{V} \frac{\partial V}{\partial T}##; ##c_P=\frac{T}{N} \frac{\partial S}{\partial T}## at constant ##P##; ##\kappa_T=\frac{–1}{V} \frac{\partial V}{\partial P}## at constant ##T##
Hi
All the expressions for calculating the properties are given in terms of ##S##, ##V## and ##N##. Should I find the energetic representation and then apply the formulas, or is there another way?
Then, for finding the energetic representation, I know that
##A=U–TS–\mu N##
But I want all these variables to be written in terms of ##S##, ##V## and ##N##. How can I do that? I also know that I can differentiate to obtain the equations of state, but these ones will be written in terms of ##T##, ##V## and ##\mu## too.
All the expressions for calculating the properties are given in terms of ##S##, ##V## and ##N##. Should I find the energetic representation and then apply the formulas, or is there another way?
Then, for finding the energetic representation, I know that
##A=U–TS–\mu N##
But I want all these variables to be written in terms of ##S##, ##V## and ##N##. How can I do that? I also know that I can differentiate to obtain the equations of state, but these ones will be written in terms of ##T##, ##V## and ##\mu## too.