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An adiabatic cylinder of cross section A...

An adiabatic cylinder of cross section A is fitted with a mass less conducting piston of thickness d and thermal conductivity K. Initially, a monatomic gas at temperature `T_(0)` and pressure `P_(0)` occupies a volume `V_(0)` in the cylinder. The atmospheric pressure is `P_(0)` and the atmospheric temperature is `T_(1) (gt T_(0))`. Find
(a) the temperature of the gas as a function of time
(b) the height raised by the piston as a function of time.
Neglect friction and heat capacities of the container and the piston.

Text Solution

Verified by Experts

The correct Answer is:
(a) `T=T_(1)-(T_(1)-T_(0))e^(-betat)`
`(b) Delta h=(V_(0)(T_(1)-T_(0))/(AT_(0))[1-e^(-betat)]` where `beta=(2T_(0)KA)/(5P_(0)V_(0)d)`
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