NEET-XII-Physics
24: Kinetic Theory of Gases
- #31Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are pA, TA, V in the vessel A and pB, TB, V in the vessel B. The vessels are now connected through a small tube. Show that the pressure p and the temperature T satisfy
pT=12pATA+pBTBwhen equilibrium is achieved.
Figure
Ans : `` \begin{array}{l}\\ {\text{Let the partial pressure of the gas in chamber A and B be P}}_{A}^{\text{'}}{\text{and P}}_{B}^{\text{'}}\text{, respectively.}\\ \\ \text{Applying equation of state for gas A, we get}\\ \frac{{P}_{A}V}{{T}_{A}}=\frac{{P}_{A}^{\text{'}}2V}{T}\\ \Rightarrow {P}_{A}^{\text{'}}=\frac{{P}_{A}T}{2{T}_{A}}\\ \text{Similarly, for gas B:}\\ {P}_{B}^{\text{'}}=\frac{{P}_{B}T}{2{T}_{B}}\\ \text{Total pressure is the sum of the partial pressures. It is given by}\\ P={P}_{A}^{\text{'}}+{P}_{B}^{\text{'}}\\ =\frac{{P}_{A}T}{2{T}_{A}}+\frac{{P}_{B}T}{2{T}_{B}}\\ \Rightarrow P=\frac{T}{2}(\frac{{P}_{A}}{{T}_{A}}+\frac{{P}_{B}}{{T}_{B}})\\ \Rightarrow \frac{P}{T}=\frac{1}{2}(\frac{{P}_{A}}{{T}_{A}}+\frac{{P}_{B}}{{T}_{B}})\end{array}``
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