A rigid vessel initially contains N moles of a diatomic gas at temperature T . Heat is supplied to the vessel, causing 50 % of the diatomic molecules to dissociate into individual atoms, and the temperature of the gas rises to 2T . Neglecting all vibrational modes, the ratio of the final internal energy of the system to its initial internal energy is:

Step-by-step solution

The initial internal energy of N moles of a diatomic gas (degrees of freedom f=5 ) at temperature T is: U_i = 5 2 NRT When 50 % of the gas dissociates, the number of moles of diatomic gas remaining is 0.5N . Each dissociated diatomic molecule yields two monoatomic atoms. Therefore, the number of moles of monoatomic gas formed is 0.5N 2 = 1.0N . In the final state, the temperature is 2T . The mixture consists of 0.5N moles of diatomic gas ( f=5 ) and 1.0N moles of monoatomic gas ( f=3 ). The final internal energy U_