`10` litre of a monoatomic ideal gas at `0^(@)C` and `10 atm` pressure is suddenly released to `1 atm` pressure and the gas expands adiabatically against this constant pressure. The final volume `(L)` of the gas.

Answer

64 L

Explanation

This is adiabatic irreversible process, so for this process
`PV^(gamma)=` Constant, is not applicable
`W= -P_(ext)(V_(2)-V_(1))`
But for adiabatic process
`W=dU=((P_(2)V_(2)-P_(1)V_(1))/(gamma-1))`
`PV=nRT " "rArr10xx10=nxx0.082xx273rArrn=4.47` moles
`-P_(ext)(V_(2)-V_(1))=((P_(2)V_(2)-P_(1)V_(1))/(gamma-1)) " "rArr-1xx(V_(2)-10)=(1xxV_(2)-10xx10)/(1.67-1)`
`rArr (10-V_(2))=(V_(2)-100)/(0.67) " "6.7-0.67 V_(2)=V_(2)-100`
`rArr 106.7V_(2) " " V_(2)=64`