According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

The root mean square velocity of molecules of gas is

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will take to cool from 75$$^\circ$$C to 69$$^\circ$$C?