We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B filled with gas having parameters $$2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

An insulated container contains a monoatomic gas of molar mass '$$\mathrm{m}$$'. The container is moving with velocity '$$\mathrm{V}$$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

In a vessel, the ideal gas is at a pressure $$\mathrm{P}$$. If the mass of all the molecules is halved and their speed is doubled, then resultant pressure of the gas will be

The average force applied on the walls of a closed container depends on $$T^x$$ where $$T$$ is the temperature of an ideal gas. The value of '$$x$$' is