70 gms of nitrogen gas was at 50 atm and 25^(@) C. (a) It was allowed to expand isothermally against a constant external pressure of one atmopshere. Calculate Deltau.Deltaq and Deltaw assuming that gas behaves ideally. (b) Also find out the maximum work that would be obtained if the gas expanded reversibly and isothermally to one atmosphere.

70 gms of nitrogen gas was at 50 atm and 25^(@) C. (a) It was allowed

1.	70 gms of nitrogen gas was at 50 atm and 25^(@) C. (a) It was allowed to expand isothermally against a constant external pressure of one atmopshere. Calculate Deltau.Deltaq and Deltaw assuming that gas behaves ideally. (b) Also find out the maximum work that would be obtained if the gas expanded reversibly and isothermally to one atmosphere.
Answer» Solution :(a) AMOUNT of gas, `n=70/28 = 2.5` moles. INITIAL pressure, `P_(1) =50`atm Final pressure, `P_(2) = 1` atm Since the gas ideal, `DeltaU =0`, as the TEMPERATURE is constant. The work obtained `DeltaW = P_(2)(V_(2)-1V_(1)) rArr P_(2) [(NRT)/P_(2) -(nRT)/P_(1)]` `=(nRTP_(2)(P_(1)-P_(2)))/(P_(1)P_(2)) = (2.5 xx 2 xx 298 xx 1(50-1))/(50 xx 1) = 1.5` kcal. (b) the maximum work done for isothermal reversible expansion. `DeltaW = nRT ln P-(1)/P_(2) = 2.303 xx 2.5 xx 2 xx 298 log 50/1 = 5.8 kcal`