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The pressure of 6 mol N(2) gas kept in a...

The pressure of 6 mol `N_(2)` gas kept in a cylinder is 30 atm at `30^(@)C`. Suddenly the gas comes out of the cylinder due to leakage. If the atmospheric pressure and temperature and 1 atm and `30^(@)C`, then calculate the work done by the gas. Assume that the gas behave ideally.

Text Solution

Verified by Experts

The atmospheric pressure (1 atm) is very much less than the initial pressure of the gas in the cylinder (30 atm) and temperature of the gas is the same as the atmospheric temperature. So, the gas will expand isothermally and irreversible against an external pressure of 1 atm.
In an isothermal irreversible expandion, `w=-nRT(1-(P_(2))/(P_(1)))`
As per given data, `P_(1)=30atm, P_(2)=1atm,n=6`
and `T=(273+30+303K`
`therefore w=-6xx8.314xx303(1(1)/(30))=-14611.02J`.
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