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

The side of a copper cube is $$1 \mathrm{~m}$$ at $$0^{\circ} \mathrm{C}$$. What will be the change in its volume, when it is heated to $$100^{\circ} \mathrm{C}$$ ? $$\left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]$$

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