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QPages 34-37: Q5: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q5 Solution: Equal masses of air are sealed in two vessels, one of volume…

Equal masses of air are sealed in two vessels, one of volume V0V_0 and the other of volume 2V02V_0. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels. Use R=8.31 J K−1 mol−1R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** P1:P2=1:1P_1 : P_2 = 1 : 1 **Step-by-Step Explanation:** For equal masses of the same gas, n1=n2=nn_1 = n_2 = n. P1=nRT1V0=nR(300)V0P_1 = \frac{nRT_1}{V_0} = \frac{nR(300)}{V_0}, P2=nRT22V0=nR(600)2V0=nR(300)V0P_2 = \frac{nRT_2}{2V_0} = \frac{nR(600)}{2V_0} = \frac{nR(300)}{V_0}. Hence P1:P2=1:1P_1 : P_2 = 1 : 1.

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