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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_(0)A = PA`
`T = (P-P_(0))A = 3/8P_(0)A` (given)

`P = 3/8 P_(0)+P_(0)=11/8 P_(0)`
Now volume is constant by string
so, `P prop T`
Initial temperature is `T_(0)`.
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