Question

At pressure $P$ and absolute temperature $T$, a mass $M$ of an ideal gas fills a closed container of volume $V$. An additional mass $2 M$ of the same gas is added into the container and the volume is then reduced to $\frac{V}{3}$ and the temperature to $\frac{T}{3}$. If now the pressure of the gas is $n P$, then find $n$.

Answer 1

If $M_{0}$ is the molecular mass of the gas, then for initial condition
$P V=\frac{M}{M_{0}} . R T\,\,\,...(i)$
After $2 M$ mass has been added,
$P' \cdot \frac{V}{3}=\frac{3 M}{M_{0}} \cdot R \cdot \frac{T}{3}\,\,\,...(ii)$
Dividing (ii) by (i), we get
$P'=3 P'$