Write the equation relating pressure,volume,and internal energy of an ideal gas.

(N/A) For an ideal gas,the pressure $P$ and volume $V$ are related to the internal energy $U$ through the kinetic theory of gases.
According to the kinetic theory,the internal energy $U$ of an ideal gas is given by $U = \frac{f}{2} PV$,where $f$ is the number of degrees of freedom of the gas molecules.
For a monoatomic gas,$f = 3$,so $U = \frac{3}{2} PV$.
For a diatomic gas at moderate temperatures,$f = 5$,so $U = \frac{5}{2} PV$.