14g oxygen at 0∘C and 10 atm are subjected to reversible adiabatic expansion to a pressure of 1 atm. What is the work done?
P1 = 10 atm at T = 273k for 1432 mole of O2
P2 = 1 atm at T = T2k for 1432 mole of O2
For adiabatic expansion we have Tγ P1 − γ = constant
∴ (T1T2)γ = (P2P1)1 − γ
or γ = (T1T2) = (1 − γ)log(P2P1)
or 1.4 log 273T2 = (1 − 1.4)log(110)
∴ T2 = 141.4 k
Work done in adiabatic expansion = nR(γ − 1)(T2 − T1)
= 1432 × 0.0821(141.4 − 273)(1.4 − 1)
Wrev = −11.82 liter atm