From the ideal gas equation: $PV = NkT$, since Pressure times Volume = Energy, my understanding is that the total (internal) energy of $N$ molecules of a gas $= NkT$.

However from the kinetic theory equation: Average kinetic energy per molecule of gas = $\frac{3}{2} kT$ and hence the total kinetic energy for $N$ molecules = $\frac{3}{2} NkT$.

Since potential energy is considered non-existent in ideal gases, kinetic energy = internal energy. However the 2 formulae lead to different results. What is the reason for this, what am I missing?

  • 1
    $\begingroup$ Pressure x volume = energy is not a hard and fast rule. In this case, its only correct up to a factor of 2/3. $\endgroup$
    – jacob1729
    May 9 '19 at 15:51
  • 2
    $\begingroup$ Also note that rotational nor vibrational degrees of freedom, contributing to the gas molar heat capacity, do not contribute in pressure not mechanical work via p and V. $\endgroup$
    – Poutnik
    May 9 '19 at 15:55
  • 1
    $\begingroup$ Who says that the internal energy of an ideal gas (or its kinetic energy) is supposed to be PV? $\endgroup$ May 9 '19 at 17:05
  • $\begingroup$ If its not then what does the PV represent? $\endgroup$
    – IK-_-IK
    May 9 '19 at 18:41
  • $\begingroup$ It merely represents part of the equation of state PV=nRT, unrelated to the internal energy. Why to you think it is related to internal energy...simply because it has the same units?? $\endgroup$ May 9 '19 at 19:25

Actually its incorrect to think that $$PV=energy$$, just because they have same units.

Strictly speacking, its defined that $$dW=PdV$$ where $dW$ is work done in change in volume of $dV$.

So your upper derivation of kinetic energy from ideal gas equation is incorrect. The kinetic energy will be found using, equipartion law and degree of freedom.


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.