Q. 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) $\frac{2p_{1}}{T_{1} + T_{2}}$
Explanation
(a)
$\frac{p_{1}}{T_{1}} + \frac{p_{1}}{T_{1}} = \frac{p}{T_{1}} + \frac{p}{T_{2}}$
$\frac{2p_{1}}{T_{1}} = p\left( \frac{T_{1} + T_{2}}{T_{1}T_{2}} \right)$
$or\ p = \frac{2p_{1}T_{2}}{T_{1} + T_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.