If we know equation of state for ideal gas $ PV = NkT$ where $P$ stands for pressure, $V$ for volume, $N$ for number of particles, $k$ is Boltzmann constant and $T$ is temperature, how can one calculate the inner energy of ideal gas $ E = \frac{3}{2}NkT$ using only thermodynamic relations, that is first and second law combined into $dE = TdS - pdV$ and some of Maxwell relations?


closed as unclear what you're asking by user36790, Kyle Kanos, John Duffield, ACuriousMind, Gert Nov 25 '15 at 14:54

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  • $\begingroup$ there is a question(4th line) "how can one calculate the inner energy of ideal gas" $\endgroup$ – cHewap Nov 25 '15 at 8:35
  • $\begingroup$ So, highlight it; no question mark; the title is dull. I would suggest to modify your question. $\endgroup$ – user36790 Nov 25 '15 at 8:39
  • $\begingroup$ is it now better? $\endgroup$ – cHewap Nov 25 '15 at 8:54
  • $\begingroup$ You cannot derive $E=3/2 NT$ from thermodynamics. In fact, $E=5/2 NT$ for diatomic gases. The best you can do is proving $E$ does not depend on $V$. Then if you assume $C_v$ is constant, you get $E=C_v N T$. $\endgroup$ – ophelia Nov 25 '15 at 9:47