The equation of state for $5\,g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be where $R$ is the gas constant.

Find the approximate number of molecules contained in a vessel of volume $7 \text{ litres}$ at $0^{\circ}C$ and a pressure of $1.3 \times 10^{5} \text{ Pa}$.

What is the mass of $2$ litres of nitrogen gas $(N_2)$ at $22.4$ atmospheric pressure and $273\,K$?

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

The volume of a given mass of a gas at $27^{\circ} C$ and $1$ $atm$ is $100$ $cc$. What will be its volume at $327^{\circ} C$ if the pressure remains constant (in $cc$)?

An ideal gas is enclosed in a container of volume $V$ at a pressure $P$. It is being pumped out of the container by using a pump with stroke volume $v$. What is the final pressure in the container after $n$ strokes of the pump? (Assume temperature remains constant.)