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

Answer

C

Explanation

(c) Here work done is zero.
So, loss in kinetic energy=change in internal
energy of gas
`1/2mv^2=nC_vDeltaT=nR/(gamma-1)DeltaT`
`1/2mv^2=m/M R/(gamma-1) DeltaT :. DeltaT=(Mv^2(gamma-1))/(2R)K`