I want to demonstrate the formula to find the internal energy of an ideal gas. The formula is

$$U = \frac{5}{2}nRT.$$

I first tried to use the formula $U = E_c + E_p$ (Internal energy of an ideal gas is equal to the sum of the kinetic energy of all particles and the potential energy).


1 Answer 1


You do that by applying the Equipartition Theorem. This theorem says that the average value of every quadratic term in the total energy of a molecule is $kT/2$. So write down the energy of a molecule, taking into account its kinetical (which shall include center of mass and rotational terms) and potential energy (which for your case must be zero, since you are considering a rigid molecule) and you shall get five quadratic terms. Hence every molecule has $5kT/2$ on avarege. Sum up over the molecules and use $Nk=nR$, where $N$ is the number of molecules.


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