A volume v of a gas at a temperature t and a pressure p enclosed in a sphere it is connected to another sphere of volume v/2 by a tube and stopcock
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Moles of gas in 1^{st}1st sphere =\cfrac{PV}{RT_1}=RT1PV
After the stop clock is opened,
Moles of 1^{st}1st sphere =\cfrac{P_1V}{RT_1}=RT1P1V
Moles in 2^{nd}2nd sphere =\cfrac{P_1V/2}{RT_2}=RT2P1V/2
\cfrac{PV}{RT_1}=\cfrac{P_1V}{RT_1}+\cfrac{P_1V}{2RT_2}RT1PV=RT1P1V+2RT2P1V
Hence, \cfrac{P}{RT_1}=\cfrac{P_1}{RT_1}+\cfrac{P_1}{2RT_2}\\ P=(\cfrac{2PT_2}{2T_2+T_1})RT1P=RT1P1+2RT2P1P=(2T2+T12PT2)
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