We are trying to show entropy gives rise to presssure. Imagine a box with volume V...
We are trying to show entropy gives rise to presssure. Imagine a box with volume V is divided into M smaller cubic boxes with volume Vo and N particles are distributed in the box. Assuming N << M, show that P=TdS/dV can be approximated to P=NkBT/V, where V=VoxM
more so, S=KblnW(N:M)
and that the first law of thermo is TdS=U+PdV-udN, but N and U are constants
Homework Answers
According to the first law of thermodynamics: TdS = 
U +
PdV - udN
Here, U and N are constants, then the following expressions can be written.
U = 0
And dN = 0
Therefore, from the first law of thermodynamics, TdS = PdV
Hence, P = TdS/dV
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