A monoatomic gas of molar mass m is filled into an insulated container. The velocity of the gas is found to be `v_0` . What is the change in temperature of the gas, if the gas is stopped suddenly?

Options

A. `(mv_0^2)/(2R)`
B. `(mv_0^2)/(3R)`
C. `R/(mv_0^2)`
D. `(3mv_0^2)/(2R)`

Answer

B

Explanation

If the container is suddenly stopped loss in kinetic energy of gas `1/2 (mn)v_0^2` where n is number of moles of gas. Let `DeltaT` is the fall in temperature of gas, Then, `n(3/2RDeltaT)=1/2mnv_0^2DeltaT = (mv_0^2)/(3R)`