Question

Two spherical vessels of equal volume are connected by a narrow tube. The apparatus contains an ideal gas at one atmosphere and $300\, K$. Now if one vessel is immersed in a bath of constant temperature $600 \,K$ and the other in a bath of constant temperature $300 \,K$, then the common pressure will be -

Answer 1

$n _{ A }=\frac{ P _{0} V _{0}}{300 R } $
$n _{ B }=\frac{ P _{0} V _{0}}{300 R }\left( P _{0}=1 atm \right)$

$n _{ A }'=\frac{ PV _{0}}{600 R }, n _{ B }'=\frac{ PV _{0}}{300 R }$
As number of moles remain conserved
$n _{ A }+ n _{ B }= n _{ A }'+ n _{ B }'$
$\frac{ P _{0} V _{0}}{300 R }+\frac{ P _{0} V _{0}}{300 R }=\frac{ PV _{0}}{600 R }+\frac{ PV _{0}}{300 R }$
$\frac{ PV _{0}}{ R }\left(\frac{1}{600}+\frac{1}{300}\right)=\frac{2 P _{0} V _{0}}{300 R }$
$P \times \frac{3}{600}=\frac{2}{300} \times 1$
$P =\frac{2}{3} \times \frac{600}{300}=\frac{4}{3} atm$