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Question
Equal masses of air are sealed in two vessels, one of volume V0 and the other of volume 2V0. 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 JK-1 mol-1
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Solution
Let the pressure and temperature for the vessels of volume V0 and 2V0 be P1, T1 and P2 , T2, respectively.
Since the two vessels have the same mass of gas, n1 = n2 = n.
\[T_1 = 300 K\]
\[ T_2 = 600 K\]
\[\text { Using the equation of state for perfect gas, we get }\] \[PV = nRT\]
\[\text { For the vessel of volume V}_o : \]
\[ P_1 V_o = nR T_1 . . . \left( 1 \right)\]
\[\text { For the vessel of volume 2 V}_o : \]
\[ P_2 \left( 2 V_o \right) = nR T_2 . . . \left( 2 \right)\]
\[\text { Dividing eq . } \left( 2 \right) \text { by eq . } \left( 1 \right), \text { we get }\]
\[\frac{2 P_2}{P_1} = \frac{T_2}{T_1} = \frac{600}{300} = 2\]
\[ \Rightarrow \frac{P_2}{P_1} = 1\]
\[ \Rightarrow P_2 : P_1 = 1: 1\]
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