Entropy BalanceEntropy Balance

Entropy BalanceEntropy Balance

• SSinin – S – Soutout + S + Sgengen = = ΔΔSSsystemsystem

• ΔΔSSsystemsystem = S = Sfinalfinal – S – Sinitialinitial

• ΔΔSSsystemsystem = 0 = 0 if the state of the if the state of the

system does not change.system does not change.–example: steady-flow devices.example: steady-flow devices.

Energy andentropy balances.

Entropy Transfer, SEntropy Transfer, Sinin and S and Soutout

• By heat transferBy heat transfer–the only method of entropy the only method of entropy

transfer for a closed system.transfer for a closed system.

Heat transfer always results in entropy transfer of Q/Tb.

If temperature of the boundary is not constant,then need to integrate orsum.

Entropy Transfer, SEntropy Transfer, Sinin and S and Soutout

• By heat transferBy heat transfer– the only method of entropy transfer for a the only method of entropy transfer for a

closed system.closed system.– If two systems are in contact, If two systems are in contact, -S-Sout1out1 = S = Sin2in2

since there is no boundary.since there is no boundary.• By workBy work– SSworkwork = 0 = 0

• Can be used to define the difference Can be used to define the difference between work and heat transfer.between work and heat transfer.

However, state of systemchanges so entropy changes. How?

Entropy is generated inthe system by friction.

Entropy Transfer, SEntropy Transfer, Sinin and S and Soutout

• By mass flowBy mass flow–only for an open system.only for an open system.

–SSmassmass = ms = ms

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

Entropy Generation, SEntropy Generation, Sgengen

• SSgengen is a measure of the entropy created is a measure of the entropy created by irreversibilities.by irreversibilities.

• SSgengen is zero only for reversible processes.is zero only for reversible processes.– so for reversible processes, the entropy so for reversible processes, the entropy

balance is like the energy balance.balance is like the energy balance.• SSgengen is withing the system boundary only.is withing the system boundary only.– so if so if SSgengen = 0 = 0 then process is internally then process is internally

reversible but maybe not externally reversible but maybe not externally reversible.reversible.

• For total For total SgenSgen must look at system and must look at system and its immediate surroundings.its immediate surroundings.

When evaluating theentropy transfer between an extendedsystem and its surroundings, boundary temp is environment temp.

Entropy Balance for Closed SystemsEntropy Balance for Closed Systems

• No entropy transfer from mass.No entropy transfer from mass.–ΣΣQQkk/T/Tkk + S + Sgengen = S = S22 – S – S11

• If adiabatic, If adiabatic, SSgengen = S = S22 – S – S11

• For system and surroundings, For system and surroundings, (an adiabatic system)(an adiabatic system)– SSgengen = = ΔΔSSsystemsystem + + ΔΔSSsurroundingssurroundings

• Should start from the general Should start from the general form and “whittle it down”.form and “whittle it down”.

Entropy Balance for Control VolumesEntropy Balance for Control Volumes

• Again, should start with general Again, should start with general entropy balance equation and entropy balance equation and “whittle it down”.“whittle it down”.• ΣΣQQkk/T/Tkk + + ΣΣmmiissii – – ΣΣmmeessee + S + Sgengen = (S = (S22

– S– S11))systemsystem

• If a steady-flow device:If a steady-flow device:–ΣΣQQkk/T/Tkk + + ΣΣmmiissii – – ΣΣmmeessee + S + Sgengen = 0 = 0

Example 6-17 Entropy generation in a wall and in its surroundings

ΣΣQQkk/T/Tkk + + ΣΣmmiissii – – ΣΣmmeessee + S + Sgengen = (S = (S22 – S – S11))systemsystem

First take wall as system. Entropy balance is:

Sgen = 1035 W/278 K – 1035 W/293 K = .191 W/K

Next take wall and surroundingsas system. How does our entropy balance change?

Just different temperatures todivide by.

Sgen,total = .341 W/K

The sgen is due to heat transferthrough a ΔT.

Example 6-18 Entropy Generation Through a Throttling Valve

Take the throttling valve as system. Entropy balance is:

ΣΣQQkk/T/Tkk + + ΣΣmmiissii – – ΣΣmmeessee + S + Sgengen = (S = (S22 – S – S11))systemsystem Assumptions?

From energy balance: if Q = 0 and W = 0, then h2 = h1.

sgen = (s2 – s1) = .3691 kJ/kg∙K

The sgen is causedby unrestrainedexpansion.

Example 6-19 A Hot Block in a Lake

ΔS of the iron? ΔSiron = mCavln(T2/T1) = -12.65 kJ/K

ΔS of the lake? ΔSlake = Qlake/Tlake = 16.97 kJ/K

Total Sgen? Sgen = ΔSiron + ΔSlake = 4.32 kJ/K

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 Sgenfor this process?System?Where is the entropy generated?How can a wall be 100°C on oneside and 25°C on the other?