Entropy & Energy Quality 2nd law: Energy of higher quality can be converted completely into lower quality form. But not vice versa. Energy quality Q measures the versatility of different energy forms.

Entropy  Carnot cycle (reversible processes): C = any closed path Qh = heat absorbed Qc = heat rejected lukewarm: can’t do W, Q   Qh , Qc = heat absorbed C = any closed path Irreversible processes can’t be represented by a path. S = entropy [ S ] = J / K

Entropy  Contour = sum of Carnot cycles. Carnot cycle (reversible processes): Qh = heat absorbed Qc = heat rejected  Qh , Qc = heat absorbed lukewarm: can’t do W, Q  C = Carnot cycle C = any closed path Irreversible processes can’t be represented by a path. S = entropy [ S ] = J / K Contour = sum of Carnot cycles.

S = 0 over any closed path  S21 + S12= 0  S21 = S21 Entropy change is path-independent. ( S is a thermodynamic variable )

Entropy in Carnot Cycle Ideal gas： Heat absorbed: Heat rejected: Adiabatic processes： 

Irreversible Heat Transfer Cold & hot water can be mixed reversibly using extra heat baths. T1 = some medium T. reversible processes T2 = some medium T. Actual mixing, irreversible processes

Adiabatic Free Expansion Adiabatic  Qad.exp. = 0    S can be calculated by any reversible process between the same states. isothermal p = const. Can’t do work Q degraded.

Entropy & Availability of Work Before adiabatic expansion, gas can do work isothermally After adiabatic expansion, gas cannot do work, while its entropy increases by  In a general irreversible process Coolest T in system

A Statistical Interpretation of Entropy Gas of 2 molecules occupying 2 sides of a box Microstates Macrostates probability of macrostate 1/4 2 ¼ = ½ 1/4

probability of macrostate Gas of 4 molecules occupying 2 sides of a box Microstates Macrostates probability of macrostate 1/16 = 0.06 4 1/16 = ¼ =0.25 6 1/16 = 3/8 = 0.38 4 1/16 = ¼ =0.25 1/16 = 0.06

Gas of 100 molecules Gas of 1023 molecules Equal distribution of molecules Statistical definition of entropy :  # of micro states

Entropy & the 2nd Law of Thermodynamics in any closed system S can decrease in an open system by outside work on it. However, S  0 for combined system.  S  0 in the universe Universe tends to disorder Life ?