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The pressure of 3 mol of an ideal gas is...

The pressure of 3 mol of an ideal gas is 10 atm at `27^(@)C`. Calculate work done by the gas when it is expanded isothermally against an external pressure of 1 atm.

Text Solution

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As per givne data, the intial pressure of the gas, `P_(1)=10`atm and the gas is expanded against an external pressure of 1 atm. Therefore, the final pressure, `P_(2)=1` atm.
Since the external pressure is very much less than the initial pressure, the gas will expand irreversibly and after expansion the pressure of the gas will be equal to the external pressure i.e., 1 atm.
In an isothermal irreversible expansion,
`w=-nRT(1-(P_(2))/(P_(1)))`
Here, `n=3,T=(273+27)K=300K`
`therefore w=-3xx8.314xx300(-1(1)/(10))=-6734.34J`
Therefore, work done by the gas in this isothermal irreversible expansion=6734.34J.
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