A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1 . 4 . Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : ( R = universal gas constant)

Step-by-step solution

KE of the vessel = 1 2 m v 2 When the vessel is suddenly stopped, the ordered motion of the gas molecules is converted into disordered motion of the molecules increasing thereby the internal energy of the gas. Thus, ∆ U = n C v ∆ T = 1 2 m v 2 = 1 2 n M v 2 Where n is number of moles of the gas in the vessel and M is molecular weight of the gas. ∴     ∆ T = M v 2 2 C v As C v = R γ - 1 ∴     ∆ T = M v 2 ( γ - 1 ) 2 R = M v 2 ( 1 . 4 - 1 ) 2 R = M v 2