Energy of all molecules of a monatomic gas having a volume V and pressure P is `3//2PV`. The total translational kinetic energy of all molecules of a diatomic gas at the same volume and pressure is

Options

A. `1//2PV`
B. `3//2PV`
C. `5//2PV`
D. `3PV`

Answer

C

Explanation

Energy of 1 mol of gas = `(f)/(2)RT=(f)/(2)PV`
where f = degrees of freedom
Montomic or diatomic gases posses equal degree of freedom for translational motion and that is equal to 3, i.e., `f=3`
`therefore E=(3)/(2)PV`
Although total energy will be different
For monatomic gas, `E_("total")=(3)/(2)PV" "("As" f=3)`
For diatomic gas, `E_("total")=(5)/(2)PV" "("As" f=5)`