A thermally insulated rigid container holds an ideal diatomic gas ( = 1.4 ). Initially, the root-mean-square (rms) speed of the gas molecules is u . The container is moving with a macroscopic speed v and is suddenly stopped. Assuming no heat loss to the surroundings, the final rms speed of the gas molecules after the container is stopped is :

Step-by-step solution

For an ideal diatomic gas, the molar heat capacity at constant volume is C_v = R - 1 = R 1.4 - 1 = 5 2 R . The internal energy of n moles of the gas at temperature T is U = n C_v T = 5 2 n R T . The rms speed of the gas molecules is given by u = 3 R T M , which implies R T = M u^2 3 . Substituting this into the internal energy expression, we get : U = 5 2 n ( M u^2 3 ) = 5 6 n M u^2 When the container moving with speed v is suddenly stopped, its macroscopic kinetic energy is converted into internal energy. The incr