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Laws of Thermodynamics
GATE 2011
Medium
Minimum work (W) required to separate a binary gas mixture at a temperature T0 and pressure P0 is W=−RT0[y1ln(f̂1/f_pure,1)+y2ln(f̂2/f_pure,2)], where y1,y2 are mole fractions, f_pure,i are fugacities of pure species, and f̂i are fugacities of species in the mixture. If the mixture is ideal then W is
- A0
- −RT0[y1 ln y1 + y2 ln y2]
- CRT0[y1 ln y1 + y2 ln y2]
- DRT0
Explanation
For an ideal mixture, f̂i=yi·f_pure,i (Lewis-Randall rule), so ln(f̂i/f_pure,i)=ln(yi). Substituting: W=−RT0[y1lny1+y2lny2], which is always positive since lnyi<0 for yi<1 — consistent with separation always requiring positive work.
Source: GATE CH 2011 (2011)
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