Question

Two vessels are connected by a valve of negligible volume. One container $\left(I\right)$ has $2.8g$ of $N_2$ at temperature $T_1\left(K\right)$. The other container $\left(II\right)$ is completely evacuated. The container $\left(I\right)$ is heated to $T_2\left(K\right)$ while container $\left(II\right)$ is maintained at $T_2/3\left(K\right)$. Volume of vessel $\left(I\right)$ is half that of vessel $\left(II\right)$. If the valve is opened, then the value of $W_I+W_{II}$ is ______.

Answer 1

Let $x$ mole of $N_2$ present into vessel $II$ and $P$ is final pressure of $N_2$
$P\left(2V\right)=xR\left(T_2/3\right)$ and $P\left(V\right)=(0.1-x)R{T}_2$
$\Rightarrow 2=\frac{x}{3(0.1-x)}$
$\Rightarrow x=0.6/7mole$;
$\frac{0.6}{7}\times 28=2.4g{N}_2$
$II$ has $2.4g{N}_2$ and $I$ has $0.4g{N}_2$;
$\frac{W_I}{W_{II}}=\frac{0.4}{2.4}=1:6$
So, value of $W_I+W_{II}=1+6=7$