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))/(rgammaR)Mv^(2)K`
B. `(gammaMv^(2))/(2R)K`
C. `((gamma-1))/(2R)mv^(2)K`
D. `((gamma-1))/(2(gamma+1)R)Mv^(2)K`

Answer

C

Explanation

Here, `(C_(p))/(C_(v))= gamma or C_(p)= gammaC_(v)`
Also `C_(p)-C_(v)= R or gammaC_(v)-C_(v)=R`
or `C_(v)=R/(gamma-1)`
no. of moles of ideal gas of mass `m` in vessel, `n=m/M` and dT kelvin be the rise in temperature,
then `1/2 mv^(2)= nC_(v)dT= m/MxxR/(gamma-1)dT`
or `dT= (M(gamma-1)V^(2))/(2R)K`.