1
$\begingroup$

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?

$\endgroup$

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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