1
$\begingroup$

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?

$\endgroup$
2
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

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 - $$ H = E+PV=\frac{3}{2}PV+PV=\frac{5}{2}PV=\frac{5}{2} \frac{2}{3}E=\frac{5}{3}E $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.