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n moles of a gas are filled in a container at temperature T. If the gas is slowly and isothermally compressed to half its initial volume, the work done by the atmosphere on the gas is

A

`(nRT)/2`

B

`-(nRT)/2`

C

`nRT(ln 2-1/2)`

D

`-nRT//n 2`

Text Solution

Verified by Experts

The correct Answer is:
A
Work done by atmosphere `P_(atm) DeltaV`
`=P_(aim)V/2.....(i)`
As, Initially gas in container is in thermodynamic equilibrium with its surroundings. `:. ` pressure inside cylinder `=P_(atm)`
& PV=nRT
`rArr P_(atm) V=nRT ` or `V=(nRT)/(P_(atm))`
Putting in (i)
`W=(nRT)/2`
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