Initially a gas of diatomic molecules is contained in a cylinder of volume V₁ at a pressure P₁ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V₁ is given by P₂ . The ratio $${{{P_2}} \over {{P_1}}}$$ is ________.

Nitrogen gas is at 300^oC temperature. The temperature (in K) at which the rms speed of a H₂ molecule would be equal to the rms speed of a nitrogen molecule, is _______.
(Molar mass of N₂ gas 28 g).

The change in the magnitude of the volume of an ideal gas when a small additional pressure $$\Delta $$P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $$\Delta $$T at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively.
If |$$\Delta $$T| = C|$$\Delta $$P| then value of C in (K/atm.) is _________.

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.