An insulated container contains a monoatomic gas of molar mass 'm'. The container is moving with velocity 'V'. If it is stopped suddenly, the change in temperature of the gas is (R-gas constant)

Step-by-step solution

Let the number of moles of the gas be n . Total mass of the gas is M = nm . The initial kinetic energy of the gas due to the motion of the container is K = 1 2 M v^2 = 1 2 nm v^2 . When the container is suddenly stopped, this kinetic energy is completely converted into the internal energy of the gas since the container is insulated. Change in internal energy is U = n C_v T . For a monoatomic gas, C_v = 3 2 R . Equating the kinetic energy to the change in internal energy: 1 2 nm v^2 = n ( 3 2 R ) T T = mv^2 3R Answe