1.

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.

Answer»

`(mnv_0^2)/(3R)`
`(mv_0^2)/(3nR)`
`(mnv_0^2)/R`
`(mv_0^2)/(2R)`

Solution :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)`


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