Lisantiom

2022-09-30

Is slope of constant pressure line is same or di in liquid region and super heated region for pure substance on $S$ diagram?

Kyan Mcdonald

Beginner2022-10-01Added 6 answers

$U=T\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}S-P\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}V+\mu \phantom{\rule{thinmathspace}{0ex}}\mathrm{d}N$

We want $\frac{\mathrm{\partial}T}{\mathrm{\partial}S}$

We know $T=\frac{\mathrm{\partial}U}{\mathrm{\partial}S}$, so $\frac{\mathrm{\partial}T}{\mathrm{\partial}S}$ is the second derivative of the internal energy with respect to entropy.

We want $\frac{\mathrm{\partial}T}{\mathrm{\partial}S}$

We know $T=\frac{\mathrm{\partial}U}{\mathrm{\partial}S}$, so $\frac{\mathrm{\partial}T}{\mathrm{\partial}S}$ is the second derivative of the internal energy with respect to entropy.

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