0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27 °C. Find the amount of heat energy to be supplied to the gas to double the rms speed of its molecules.
The root mean square speed is related to absolute temperature T as
For a given gas, m is fixed. Therefore, . Hence in order to double the root mean square speed, the absolute temperature must be increased to four times the initial value. Initial temperature . Therefore, final temperature .
Since the volume of the vessel is fixed, V = 0. Hence the heat energy supplied to the gas does no work on the gas; it only increases the internal energy of the molecules.