• # question_answer Two closed vessels of equal volume containing air at pressure ${{P}_{1}}$ and temperature ${{T}_{1}}$ are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at ${{T}_{1}}$ and that in the other at ${{T}_{2}}$, what will be the pressure in the vessels A)                 $\frac{2{{P}_{1}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}$              B)                 $\frac{{{T}_{1}}}{2{{P}_{1}}{{T}_{2}}}$ C)                 $\frac{2{{P}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}$              D)                 $\frac{2{{p}_{1}}}{{{T}_{1}}+{{T}_{2}}}$

$\frac{{{P}_{1}}}{{{T}_{1}}}+\frac{{{P}_{1}}}{{{T}_{1}}}=\frac{P}{{{T}_{1}}}+\frac{P}{{{T}_{2}}}$                                 $\frac{2{{P}_{1}}}{{{T}_{1}}}=P\left( \frac{{{T}_{1}}+{{T}_{2}}}{{{T}_{1}}{{T}_{2}}} \right)$;  $\therefore P=\frac{2{{P}_{1}}({{T}_{1}}{{T}_{2}})}{{{T}_{1}}({{T}_{1}}+{{T}_{2}})}=\frac{2{{P}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}$