Question

Two identical vessel $A$ and $B$ each of volume $V_{0}$ joined together with a small tube (as shown in the figure) initially containing the same gas at pressure $P_{0}$ and absolute temperature $T_{0}$ The vessel $A$ is now heated to maintain its temperature at $2 T_{0}$ while the vessel $B$ is maintained at the same temperature $T_{n}$ .

Question Image

Find the common pressure of the gas.

Find the number of moles of the gas in each vessel.

Accepted Answer

Given, Pressure of the gas $= P_{0}$

Absolute temperature $= T_{0}$

Vessel $A$ is heated to maintain the temperature $2 T_{0}$ and vessel $B$ at temperature $T_{0}$

The total number of moles of the gas,

$n = \frac{P_{0} (2 V_{0})}{{RT}_{0}} = \frac{2 P_{0} V_{0}}{{RT}_{0}}$

Initially both the vessels contain equal number of moles. When the vessel $A$ is heated, a few moles of the gas move from vessel $A$ to $B$ Let $n_{A}$ and $n_{B}$ be the final number of moles present in $A$ and $B$ , respectively, then

$n_{A} {RT}_{A} = n_{B} {RT}_{B} = PV =$ constant

$\frac{n_{A}}{n_{B}} = \frac{T_{B}}{T_{A}} = \frac{T_{0}}{2 T_{0}} = \frac{1}{2}$

Thus $n_{A} = \frac{n}{3} = \frac{2 P_{0} V_{0}}{3 {RT}_{0}}$ and $n_{B} = \frac{2}{3} n = \frac{4 P_{0} V_{0}}{3 {RT}_{0}}$

B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS

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