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Question
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
What is the final pressure of the gas in A and B?
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Solution 1
0.5 atm
The volume available to the gas is doubled as soon as the stopcock between cylinders A and B is opened. Since volume is inversely proportional to pressure, the pressure will decrease to one-half of the original value. Since the initial pressure of the gas is 1 atm, the pressure in each cylinder will be 0.5 atm.
Solution 2
Since the final temperature and initial temperature remain the same,
`therefore "P"_2"V"_2 = "P"_1"V"_1`
But P1 = 1 atm, v1 = V, V2 = 2V and P2 = ?
`therefore "P"_2 = ("P"_1"V"_1)/"V"_2 = (1xx"V")/"2V"`
= 0.5 atm
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