A gas is compressed at a constant pressure of $$50 \mathrm{~N} / \mathrm{m}^2$$ from a volume of $$10 \mathrm{~m}^3$$ to a volume of $$4 \mathrm{~m}^3$$. Energy of $$100 \mathrm{~J}$$ is then added to the gas by heating. Its internal energy is

The pressure exerted by an ideal gas at a particular temperature is directly proportional to

The temperature of an ideal gas is increased from $$27^{\circ} \mathrm{C}$$ to $$927^{\circ} \mathrm{C}$$. The r.m.s. speed of its molecules becomes

A jar '$$\mathrm{P}$$' is filled with gas having pressure, volume and temperature $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ respectively. Another gas jar $$Q$$ filled with a gas having pressure $$2 \mathrm{P}$$, volume $$\frac{\mathrm{V}}{4}$$ and temperature $$2 \mathrm{~T}$$. The ratio of the number of molecules in jar $$\mathrm{P}$$ to those in jar $$Q$$ is