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A cylinder fitted with a piston contains...

A cylinder fitted with a piston contains an ideal gas with a volume of 21 L. the gas is compressed isothermally to 1/3 rd of its initial volume under a constant external pressure of 3 atm. Calculate q, w and `DeltaU`.

Text Solution

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Work done, `w=-P_(ex)(V_(2)-V_(1))[V_(1)gtV_(2)]`
Given: `P_(ex)=3atm,V_(1)=21L and V_(2)=21xx(1)/(3)=7L`
`therefore w=-3(7-21)=42L*atm`
`=42xx101.3J=4254.6J" "[because 1L*atm=101.3J]`
In an isothermal process of an ideal gas, the internal energy of the gas does ot change i.e., `DeltaU=0`
From the first law of thermodynamics, `DeltaU=q+w`
`therefore 0=q+425.6J or, q=-4254.6J`
thus, in the process `q=-4254.6J, w=+4254.6J,DeltaU=0`.
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