An insulated container containing n moles of monoatomic gas of molar mass m is moving with a velocity `v_0`. If the container is suddenly stopped, find the change in temperature.

Options

A. `(mnv_0^2)/(3R)`
B. `(mv_0^2)/(3nR)`
C. `(mnv_0^2)/R`
D. `(mv_0^2)/(2R)`

Answer

A

Explanation

There is n moles of the monoatomic gas in the container.
molar mass of the gas = m,
Total mass of the gas in the container, M=mn
Change in KE of the gas when the container is suddenly stopped, i.e,
`DeltaK=(KE)_"initial"-(KE)_"final"=1/2Mv_0^2-0=1/2Mv_0^2 = 1/2 mnv_0^2`
This change in kinetic energy (`DeltaK`) result in a change in internal energy (`DeltaU`) of the gas.
`DeltaU=nC_VDeltaT=n(3/2R)DeltaT`
Here, `DeltaT` is the change in temperature of the gas.
As `DeltaU=DeltaK, n(3/2 R)DeltaT=1/2mnv_0^2 therefore DeltaT=(mnv_0^2)/(3R)`