Question

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. $\frac{2P_{1} T_{1}}{T_{1}+T_{2}}$
• B. $\frac{T_{1}}{2P_{1}T_{2}}$
• C. $\frac{2P_{1}T_{2}}{T_{1}+T_{2}}$
• D. $\frac{2P_{1}}{T_{1}+T_{2}}$

Answer 1

Answer: (C)

$\frac{P_{1}}{T_{1}}+\frac{P_{1}}{T_{1}}=\frac{P}{T_{1}}+\frac{P}{T_{2}}$
$\frac{2P_{1}}{T_{1}}=P\left(\frac{T_{1} +T_{2}}{T_{1}T_{2}}\right)$
$\therefore P=\frac{2P_{1}\left(T_{1}T_{2}\right)}{T_{1}\left(T_{1}+T_{2}\right)}=\frac{2P_{1}T_{2}}{T_{1}+T_{2}}$