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Entropy Balance

Entropy Balance. Entropy Balance. S in – S out + S gen = Δ S system Δ S system = S final – S initial Δ S system = 0 if the state of the system does not change. example: steady-flow devices. Energy and entropy balances. Entropy Transfer, S in and S out. By heat transfer

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Entropy Balance

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  1. Entropy Balance

  2. Entropy Balance • Sin – Sout + Sgen = ΔSsystem • ΔSsystem = Sfinal – Sinitial • ΔSsystem = 0 if the state of the system does not change. • example: steady-flow devices.

  3. Energy and entropy balances.

  4. Entropy Transfer, Sin and Sout • By heat transfer • the only method of entropy transfer for a closed system.

  5. Heat transfer always results in entropy transfer of Q/Tb. If temperature of the boundary is not constant, then need to integrate or sum.

  6. Entropy Transfer, Sin and Sout • By heat transfer • the only method of entropy transfer for a closed system. • If two systems are in contact, -Sout1 = Sin2 since there is no boundary. • By work • Swork = 0 • Can be used to define the difference between work and heat transfer.

  7. Entropy is generated in the system by friction. However, state of system changes so entropy changes. How?

  8. Entropy Transfer, Sin and Sout • By mass flow • only for an open system. • Smass = ms

  9. Mass contains entropy as well as energy so produces both entropy and energy transfer.

  10. Entropy Generation, Sgen • Sgenis a measure of the entropy created by irreversibilities. • Sgenis zero only for reversible processes. • so for reversible processes, the entropy balance is like the energy balance. • Sgenis withing the system boundary only. • so if Sgen = 0 then process is internally reversible but maybe not externally reversible. • For total Sgen must look at system and its immediate surroundings.

  11. When evaluating the entropy transfer between an extended system and its surroundings, boundary temp is environment temp.

  12. Entropy Balance for Closed Systems • No entropy transfer from mass. • ΣQk/Tk + Sgen = S2 – S1 • If adiabatic, Sgen = S2 – S1 • For system and surroundings, (an adiabatic system) • Sgen = ΔSsystem + ΔSsurroundings • Should start from the general form and “whittle it down”.

  13. Entropy Balance for Control Volumes • Again, should start with general entropy balance equation and “whittle it down”. • ΣQk/Tk + Σmisi – Σmese + Sgen = (S2 – S1)system • If a steady-flow device: • ΣQk/Tk + Σmisi – Σmese + Sgen = 0

  14. Example 6-17 Entropy generation in a wall and in its surroundings First take wall as system. Entropy balance is: ΣQk/Tk + Σmisi – Σmese + Sgen = (S2 – S1)system Sgen = 1035 W/278 K – 1035 W/293 K = .191 W/K Next take wall and surroundings as system. How does our entropy balance change? Just different temperatures to divide by. Sgen,total = .341 W/K The sgen is due to heat transfer through a ΔT.

  15. Example 6-18 Entropy Generation Through a Throttling Valve Take the throttling valve as system. Entropy balance is: Assumptions? ΣQk/Tk + Σmisi – Σmese + Sgen = (S2 – S1)system From energy balance: if Q = 0 and W = 0, then h2 = h1. sgen= (s2 – s1) = .3691 kJ/kg∙K The sgen is caused by unrestrained expansion.

  16. Example 6-19 A Hot Block in a Lake ΔSiron = mCavln(T2/T1) = -12.65 kJ/K ΔS of the iron? ΔS of the lake? ΔSlake = Qlake/Tlake = 16.97 kJ/K Total Sgen? Sgen = ΔSiron + ΔSlake = 4.32 kJ/K

  17. Example 6-21 Entropy Generation Associated with Heat Transfer What do we take as a system? What are our assumptions? With the water as our system, isothermal, internally reversible.. What is Sgen? What is ΔS of the system? How do we get the total Sgen for this process? System? Where is the entropy generated? How can a wall be 100°C on one side and 25°C on the other?

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