A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats `gamma`. It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Options

A. `((gamma-1))/(2(gamma+1)R)Mv^2`
B. `((gamma-1)/(2gammaR))Mv^2`
C. `(gammaMv^2)/(2R)`
D. `((gamma-1)/(2R))Mv^2`

Answer

D

Explanation

`0=DeltaU+DeltaW`
`nC_VDeltaT-(1)/(2)Mv^2=0`
`DeltaT=((1)/(2)Mv^2)/(nC_V)=((1)/(2)MV62)/(((nR)/(gamma-1)))`
`=(1)/(2)((gamma-1)Mv^2)/(nR)=(1)/(2)((gamma-1)Mv^2)/(R)`
`(n=1)`