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The air tight and smooth piston of a cyl...

The air tight and smooth piston of a cylindrical vessel are connected with a string as shown. Initially pressure and temperature of the gas are `P_(0)` and `T_(0)`. The atmospheric pressure is also `P_(0)`. At a later time, tension in the string is `(3)/(8) P_(0)A` where A is cthe cross-sectional are of the cylinder. at this time, the temperature of the gas has become.

A

`(3)/(8)T_(0)`

B

`(3)/(4)T_(0)`

C

`(11)/(8)T_(0)`

D

`(13)/(8)T_(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
`T=P_(o)A=PA T=(P-P_(0))A`
`=(3)/(2)P_(0)A("given")P=(3)/(8)P_(0)+P(11)/(8)P_(0)`
Now volume is constnat by string So, `PalphaT`
Initial temperature is `T_(0)`
Now a spressure has become `(11)/(8)P_(0)`.
temperature will be `(11)/(8)T_(0)`
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