Question

Two closed containers of equal volume filled with air at pressure $P_{0}$ and temperature $T_{0}$. Both are connected by a narrow tube. If one of the container is maintained at temperature $T_{0}$ and other at temperature $T$, then new pressure in the containers will be

• A. $\frac{2 P_{0} T}{T+T_{0}}$
• B. $\frac{P_{0} T}{T+T_{0}}$
• C. $\frac{P_{0} T}{2\left(T+T_{0}\right)}$
• D. $\frac{T+T_{0}}{P_{0}}$

Answer 1

Answer: (A)

$\frac{P}{T}=$ constant
Initially $\frac{P_{0}}{T_{0}}+\frac{P_{0}}{T_{0}}=\frac{2 P_{0}}{T_{0}}$
For two containers
$\frac{P_{0}}{T_{0}}+\frac{P}{T}=\frac{2 P_{0}}{T_{0}}$
$P=\frac{2 P_{0} \times T \times T_{0}}{T_{0}\left(T+T_{0}\right)}$
or $P=\frac{2 P_{0} T}{\left(T+T_{0}\right)}$