Question

Energy of all molecules of a monoatomic gas having a volume V and pressure P is $\frac{3}{2}PV$. The total translational kinetic energy of all molecules of a diatomic gas as the same volume and pressure is

• A. $\frac{1}{2}PV$
• B. $\frac{3}{2}PV$
• C. $\frac{5}{2}PV$
• D. 3 PV

Answer 1

Answer: (B)

$\frac{3}{2}PV$

Answer 2

Energy of 1 mole of gas $= \frac{f}{2}RT = \frac{f}{2}PV$

where f = Degree of freedom

Monoatomic or diatomic both gases posses equal degree of freedom for translational motion and that is equal to 3 i.e.

f = 3

∴ $E = \frac{3}{2}PV$

Although total energy will be different, For monoatomic gas $E_{\text{total}} = \frac{3}{2}PV$ [As f = 3]

For diatomic gas $E_{\text{total}} = \frac{5}{2}PV$ [As f = 5]