How to calculate the energy and entropy content of an amount of substance?
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If you're searching for the entropy S(T,V,N)S(T,V,N) as a function of volume VV, temperature TT and number of particles NN, then you can find an easy relation with heat capacity:
CV=T(∂S∂T)V,NCV=T(∂S∂T)V,N
You can find this observation for example in the book of Landau (fifth volume §13), but almost in each book of thermodynamics. It derives from the definition of CVCV and thermodynamic potentials:
S=−(∂F∂T)V,N=−(∂G∂T)p,N=−(∂Ω∂T)V,μS=−(∂F∂T)V,N=−(∂G∂T)p,N=−(∂Ω∂T)V,μ
For the explicit calculus of entropy you to find over of those potentials express in terms of their own thermodynamic variables:
F=F(V,T,N)F=F(V,T,N)
Ω=Ω(V,T,μ)Ω=Ω(V,T,μ)
G=G(p,T,N)G=G(p,T,N)
where μμ is the chemical potential, pp there pressure.
CV=T(∂S∂T)V,NCV=T(∂S∂T)V,N
You can find this observation for example in the book of Landau (fifth volume §13), but almost in each book of thermodynamics. It derives from the definition of CVCV and thermodynamic potentials:
S=−(∂F∂T)V,N=−(∂G∂T)p,N=−(∂Ω∂T)V,μS=−(∂F∂T)V,N=−(∂G∂T)p,N=−(∂Ω∂T)V,μ
For the explicit calculus of entropy you to find over of those potentials express in terms of their own thermodynamic variables:
F=F(V,T,N)F=F(V,T,N)
Ω=Ω(V,T,μ)Ω=Ω(V,T,μ)
G=G(p,T,N)G=G(p,T,N)
where μμ is the chemical potential, pp there pressure.
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calculate the change in entropy. The standard thermodynamic relation is
dU=TdS−PdVdU=TdS−PdV
where dUdU refers to change in Internal energy, TT temperature, dSdS change in entropy, PP Pressure and dVdV change in volume. For fixed volume, the equation gives
dS=dUT
dU=TdS−PdVdU=TdS−PdV
where dUdU refers to change in Internal energy, TT temperature, dSdS change in entropy, PP Pressure and dVdV change in volume. For fixed volume, the equation gives
dS=dUT
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