Initially, the root mean square (rms) velocity of N₂ molecules at certain temperature is $$u$$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

At very high pressures, the compressibility factor of one mole of a gas is given by :

Two closed bulbs of equal volume $$(V)$$ containing an ideal gas initially at pressure $${p_i}$$ and temperature $${T_1}$$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $${T_2}.$$ The final pressure $${p_f}$$ is :

If Z is a compressibility factor, van der Waals equation at low pressure can be written as: