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

Answer

D

Explanation

`(1)/(2)Mv^(2) = C_(v)DeltaT`
`(1)/(2)Mv^(2) = (R )/(gamma-1) DeltaT`
`DeltaT = (Mv^(2)(gamma-1))/(2R) = ((gamma-1)Mv^(2))/(2R)`