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Question

Air is filled at 60C in a vessel of open mouth. The vessel is heated to a temperature T, so that 14th part of the air escapes. Assuming the volume of the vessel remains constant, the value of T is

A
80C
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B
44C
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C
333C
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D
171C
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Solution

The correct option is D 171C
Mass of the air left in the vessel MM4=3M4
(as 14th part of air escapes)
Given, initial temperature T1=60C=333 K

PV=nRT [Ideal gas equation ]
PV=(MMolecular Mass)RT
Pressure and volume of the gas remain constant. [because vessel is open to atmosphere, pressure will be the same as atmospheric pressure]
i.e MT= constant.
T2T1=M1M2=⎜ ⎜ ⎜M3M4⎟ ⎟ ⎟=43
T2=43×T1=43×333=444 K=171C

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