I am trying to find a formula for tying things up. Given an ideal gas like helium or nitrogen gas (diatomic) how can I find its enthalpy simply given internal energy?

I remember it was once taught in thermodynamics class but I cannot find the reference material anymore; I've tried searching on the net too.

I tried tying things up though:

PV = mRT
H = U + PV
H = U + mRT

Is this right? Am I missing anything? is there another more elegant way?


The internal energy of a system is directly proportional to its temperature. Formally, $$E_{sys}=\frac{3}{2}RT. $$ You could then note that $$PV=nRT=H_{sys}-E_{sys},$$ or $$H_{sys}=RT\bigg(\frac{3}{2}+n\bigg)$$ or, identically, $$H_{sys}=\frac{3}{2}RT +PV. $$ Your method should work, however, this is in my opinion a more "elegant" solution.

  • $\begingroup$ You missed the $n$ in your $E_{sys}$ expression. Which will change your expression for $H_{sys}$ slightly. $\endgroup$ – JoDraX Jul 5 '15 at 21:12

Ideal gas equation of state - $$ PV = Nk_bT $$ For ideal gas (can be calculated directly from entropy (Sakur-Tetrode) or via equipartition theorem) - $$ E = \frac{3}{2}Nk_bT=\frac{3}{2}PV $$ thus - $$ H = E+PV=\frac{3}{2}PV+PV=\frac{5}{2}PV=\frac{5}{2} \frac{2}{3}E=\frac{5}{3}E $$


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