$A$ cylinder contains hydrogen gas at a pressure of $249\; kPa$ and temperature $27^{\circ} C$. Its density is $............. kg/m^{3}$ $(R = 8.3\; J\; mol^{-1} K^{-1})$.

On which does the value of $\alpha_V$ depend for an ideal gas?

$Assertion :$ One mole of any substance at any temperature or volume always contains $6.02 \times 10^{23}$ molecules.
$Reason :$ One mole of a substance always refers to $S.T.P.$ conditions.

One mole of a gas at a pressure $2 \ Pa$ and temperature $27^{\circ} C$ is heated until both pressure and volume are doubled. What is the final temperature of the gas (in $K$)?

State Boyle's law and Charles's law.

An insulated container is divided into two parts by a partition. The same gas is filled in both parts. In the right part,the volume,temperature,and pressure are $2V$,$T$,and $2P$ respectively. In the left part,the same parameters are $V$,$T$,and $P$. What is the ratio of the number of molecules in the right part to the left part?