Internal Energy is a state variable and its value at a particular state cannot be measured; only the change in internal energy can be measured. So how come we write that
$U$ = internal energy of the system,
$n$ = no of moles of the gas,
$R$ = Universal gas constant,
$T$ = Temperature of the system.

Till now, I knew that it was 'Avg Kinetic energy' that followed the above relation that is $\mathrm{K.E.} = (3/2)nRT$, but today while looking at a video in Khan Academy, I came across the relation $U=(3/2)nRT$ and got entirely confused.

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    $\begingroup$ Internal Energy is (3/2)nRT plus some constant that cannot be measured. $\endgroup$ – Ivan Neretin Feb 13 '18 at 17:06
  • $\begingroup$ @IvanNeretin That constant can be approximated to be zero is it? Because in high school physics we just use 3/2 nRT. $\endgroup$ – KV18 May 7 at 13:45
  • $\begingroup$ "Approximated" is a wrong word. Let's say it can be assumed to be 0. $\endgroup$ – Ivan Neretin May 7 at 13:46

Molecules have internal energy due to intermolecular interactions, as well as translational kinetic energy, rotational energy, vibrational energy, electronic energy (and if you care to include them, nuclear energy and the mass-energy of the protons, neutrons and electrons themselves).

By saying "ideal", energy due to intermolecular interactions is eliminated.

By saying "monoatomic", energy due to rotation and vibration is eliminated.

So only translational kinetic energy and electronic energy remains.

(3/2)nRT is the translational kinetic energy, and since almost all atoms are in the ground electronic state at low temperature, it is a good expression for internal energy as long as the temperature is low enough that essentially all atoms are in the electronic ground state.


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