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Question

Two identical vessels contain the same gas at pressures P1 and P2 at absolute temperatures T1 and T2 respectively. On joining the vessels with a small tube, the gas reaches a common temperature T and a common pressure P. Determine the ratio P/T.

A

P1T1 + P2T2T1T2
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B
12(P1T1 + P2T2T1T2]
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C
12(P1T2 + P2T1T1T2]
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D
P1T2 + P2T1T1T2
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Solution

The correct option is C 12(P1T2 + P2T1T1T2]
On combining the vessels, the total number of moles remains constant
i.e
n=n1 + n2
Using the ideal gas equation, we can write
n1=P1VRT1
n2=P2VRT2
and n = P(2V)RT
where V is the volume of each vessel.
Thus,
P(2V)RT = P1VRT1 + P2VRT2or PT = 12(P1T1+P2T2] = 12(P1T2 +P2T1T1T2]

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