In an industrial process, nitrogen is heated to $500 \mathrm{~K}$ in a vessel of constant volume. If it enters the vessel at $100 \mathrm{~atm}$ and $300 \mathrm{~K}$, what pressure would it exert at the working temperature if it behaved as a perfect gas?
Cancellation of the volumes (because $V_1=V_2$ ) and amounts (because $\left.n_1=n_2\right)$ on each side of the combined gas law results in
$$
\frac{p_1}{T_1}=\frac{p_2}{T_2}
$$
which can be rearranged into
$$
p_2=\frac{T_2}{T_1} \times p_1
$$
Substitution of the data then gives
$$
p_2=\frac{500 \mathrm{~K}}{300 \mathrm{~K}} \times(100 \mathrm{~atm})=167 \mathrm{~atm}
$$
