In a certain thermodynamical process, the pressure of a gas depends on its volume as kV³. The work done when the temperature changes from 100$$^\circ$$C to 300$$^\circ$$C will be ___________ nR, where n denotes number of moles of a gas.

The root mean square speed of molecules of a given mass of a gas at 27$$^\circ$$C and 1 atmosphere pressure is 200 ms^$$-$$1. The root mean square speed of molecules of the gas at 127$$^\circ$$C and 2 atmosphere pressure is $${{x \over {\sqrt 3 }}}$$ ms^$$-$$1. The value of x will be _________.

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.

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 ________.