- #1
Adam564
- 8
- 1
- Homework Statement
- Two non-ideal gases, A and B, whose internal energies only depend on temperature obey the following equations of state $$p=\alpha_A\frac{NT}{V^2}$$ and $$p=(\beta_B\frac{N}{V}T)^{1/2}$$, respectively. Here, $$\alpha_A$$ and $$\beta_B$$ are some constants. Determine for both gases individually whether a well-defined entropy exists. If not, what does that imply?
- Relevant Equations
- $$dU=TdS-pdV$$
$$dS=\frac{dU}{T}+\frac{p}{T}dV$$
The conclusion of my attempt I am listing below is that there do exist entropies for both but I am not sure.
$$dU=TdS-pdV$$
$$dS=\frac{dU}{T}+\frac{p}{T}dV$$
Therefore, gas A:
$$S=\frac{{\Delta}U}{T}+\alpha_A(\frac{-N}{{\Delta}V})$$
Gas B:
$$S=\frac{{\Delta}U}{T}+\frac{1}{\sqrt{T}}\sqrt{\beta_B}2\sqrt{N{\Delta}V}$$
$$dU=TdS-pdV$$
$$dS=\frac{dU}{T}+\frac{p}{T}dV$$
Therefore, gas A:
$$S=\frac{{\Delta}U}{T}+\alpha_A(\frac{-N}{{\Delta}V})$$
Gas B:
$$S=\frac{{\Delta}U}{T}+\frac{1}{\sqrt{T}}\sqrt{\beta_B}2\sqrt{N{\Delta}V}$$