MTX221. Session 33 ENTROPY (CONTROL MASS) Sessie 33 ENTROPIE (KONTROLE MASSA) Dr. Jaco Dirker. These slides also appear on Click-UP

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1 Ses. 33- MTX Sessie 33 ENTROPIE (KONTROLE MASSA) Session 33 ENTROPY (CONTROL MASS) Dr. Jaco Dirker These slides also appear on Click-UP Hierdie skyfies verskyn ook op Click-UP 8 th edition / 8e uitgawe

2 Ses. 33- Die Entropie van n Suiwer Stof 6.3 The Entropy of a Pure Substance Spesifieke entropie Specific entropy is intensive (thus independent of the amount of mass) [kj/kgk] Entropy values are listed in TD tables according to some reference temp. For most refrigerants, -40ºC is used as the reference value in our Tables, BUT can be different for other TD data-sets : BE CAREFUL. (Please note: Negative entropy values are also listed) The term entropy is used for both total entropy, S, [kj/k] and specific entropy, s, [kj/kgk] refer to context. For a two-phase saturated state: s s f xs fg Totale entropie Verwysings temp.

3 Ses Die Entropie van n Suiwer Stof 6.3 The Entropy of a Pure Substance Temperature-Entropy diagrams (T-s diagrams) are of use to visualise the change of state: Another diagram also used is a Enthalpy-Entropy Diagram: Temperatuur-Entropie Diagram Entalpie-Entropie Diagram Vloeist. Liq. Gas Gas

4 Ses Die Entropie van n Suiwer Stof 6.3 The Entropy of a Pure Substance Saamgedrukte / onderverkoelde vloeist Generally for compressed liquid: Entropy is very similar to saturated Gesatureerde vloeist. Liq. entropy at the same given temp. Therefore for compressed liquid: s s f ONLY IF NO ALTERNATIVE DATA SOURCE IS AVAILABLE USE DISCRETION.

Ses. 33-5 Remember: Q ds [J/K] T Let us now consider the entropy change during the reversible processes in the Carnot cycle.

5 Ses Remember: Q ds [J/K] T Let us now consider the entropy change during the reversible processes in the Carnot cycle. (We will for now limit ourselves to reversible processes) Remember the Carnot Cycle: Isothermal Expansion Adiabatic Expansion Isothermal Compression Adiabatic Compression rev Isotermiese Uitsetting Adiabatiese Uitsetting Isotermies Samedrukking Adiabatiese Samedrukking Carnot Kringloop

6 Ses Omkeerbare Isotermiese Uitsetting met Hitte-oordrag Reversible Isothermal Expansion with heat transfer: ( ) S S Q T rev Because it is reversible (with const. temp): Note that the Heat transfer can be written as: S S * This is only true for a reversible process T Q Q H T H Q TH S S *

7 Ses Omkeerbare Adiabatiese Uitsetting Reversible Adiabatic Expansion ( 3) Adiabatic means: Q3 0 Thus: We thus have a constant entropy process (S 3 = S ) This is called an isentropic process S Q 3 3 S T rev 0 isentropiese proses

8 Ses Reversible Isothermal Compression with heat transfer: (3 4) Omkeerbare Isotermiese Samedrukking met Hitte-oordrag S Q T Q S3 3 rev T L Remember Q 0, therefore: S 4 S3 0 (Entropy decreases) 3 4

9 Ses Omkeerbare Adiabatiese Samedrukking Reversible Adiabatic Compression (4 ) Q 4 4 T rev S S 0 (Because Q = 0) Isentropic process: isentropiese proses S S 4

Ses. 33-0 Summary (Reversible processes) Isothermal

Expansion ( 3): Adiabatiese Uitsetting Isothermal

Compression (4 ): Adiabatiese Samedrukking Q S S T H S S

10 Ses Summary (Reversible processes) Isothermal Expansion ( ): Isotermiese Uitsetting Adiabatic Expansion ( 3): Adiabatiese Uitsetting Isothermal Compression (3 4): Isotermiese Samedrukking Adiabatic Compression (4 ): Adiabatiese Samedrukking Q S S T H S S 3 S 3 4 S4 S3 T L S4 0 (isentropic) Q 0 (isentropic) isentropies isentropies

11 Ses. 33- Let s plot these processes on a T-s diagram: Area under line represents heat transfer to the system, Q H Area under line 3 4 represents heat transfer from the system, Q L Area 3 4 represents the Work output for this Heat Engine Termiese Rendement: Thermal efficiency: W area _ 3 4 thermal Q area _ b a H Stip op n T-s diagram: Isothermal Adiabatic Entropy increases at T H and decreases at T L Entropie neem toe by T H en neem af by T L Heat Engine Hitte-enjin

Ses. 33- If the Heat engine cycle is reversed, we will have a refrigerator / heat pump: Note the change in direction of arrows (counter clockwise) antikloksgewys Entropy

12 Ses. 33- If the Heat engine cycle is reversed, we will have a refrigerator / heat pump: Note the change in direction of arrows (counter clockwise) antikloksgewys Entropy decreases at T H and increases at T L (Heat transfer to the system occurs at T L ) Entropie neem af by T H en neem toe by T L Refrigerator / Heat Pump Verkoeler / Hittepomp

13 Ses SPECIAL CASE: Spesiale Geval Omkeerbare hitte-oordrag proses Let s consider a general reversible heat transfer process Consider a system which is internally reversible (no irreversibility inside its boundaries) : Intern omkeerbaar Saturated liquid is heated from state to 3. From state to the process occurs at constant pressure and temperture Konst. druk en temp. Thus: s s s fg m Q T rev But But m q Q T rev mt h h h fg Q (Remember: Q m h h for const. pressure) q T Konst. druk Therefore: s s h T In this case: h s fg h T fg

14 Ses SPECIAL CASE. reversible heat transfer process In this case: h fg s fg T Let s check this: Consider saturated water at 00ºC:. This gives an indication on how entropy change can be calculated, but only for constant pressure, constant temperature processes. Konst. druk en temp ONLY valid for s fg, NOT for s f and s g entropieverandering

Ses. 33-5 SPECIAL CASE For process, the heat transfer is given by the area under line What about the heat transferred from to 3? 3 q3 Tds The heat transfer is still equal to the area under line 3.

15 Ses SPECIAL CASE For process, the heat transfer is given by the area under line What about the heat transferred from to 3? 3 q3 Tds The heat transfer is still equal to the area under line 3. Temp. nie konst. nie T is not constant, thus without the mathematical relation for T (s) this integral can not be obtained directly. IMPORTANT: Heat transfer is only equal to the area under the process line on a T-s diagram if the process is reversible. We will revisit this soon again.

16 Ses Reversible Process Entropy Change Example Based on EX6. (Ed 8), but the following is changed: Working Substance: Ammonia Evaporation temp = -0ºC Condensation temp = 70ºC Mass flow rate = 0.5 kg/s Afrikaans op volgende skyfie Consider a Carnot-cycle heat pump with Ammonia as working fluid. Heat is absorbed into the system at -0ºC (changes from a two-phase state to a saturated vapour). Heat is rejected at 70ºC until the ammonia is a saturated liquid. The Ammonia has a mass flow rate of 0.5 kg/s. Determine the following: a) Pressure after compression before heat rejection b) Quality before evaporation c) Heat receiving rate d) COP of the system.

17 Ses Omkeerbare Proses Entropieverandering Voorbeeld Gebasseer op VB6. (Wge 8), maar met wysigings: Werksvloeier: Ammoniak Verdamping temp = -0ºC Kondensasie temp = 70ºC Massavloei-tempo = 0.5 kg/s English on previous slide Beskou n Carnot-kringloop hittepomp met Ammoniak as werksvloeier. Hitte word ontvang in die stelsel teen -0ºC (verander van tweefase tot n versadigde damp). Hitte word verwerp teen 70ºC tot die ammoniak n versadigde vloeistof is. Die ammoniak het n massavloeitempo van 0.5 kg/s. Bepaal die volgende: a) Die druk na samedrukking, maar voor hitte-verwerping b) Kwaliteit voor verdamping c) Hitte-ontvangstempo d) COP van die stelsel.

MTX221. Session 36 ENTROPY (CONTROL MASS) Sessie 36 ENTROPIE (KONTROLE MASSA) Dr. Jaco Dirker. These slides also appear on Click-UP

MTX221. Session 36 ENTROPY (CONTROL MASS) Sessie 36 ENTROPIE (KONTROLE MASSA) Dr. Jaco Dirker. These slides also appear on Click-UP Ses.36- MX Sessie 36 ENROIE (KONROLE MASSA) Session 36 ENROY (CONROL MASS) Dr. Jaco Dirker hese slides also appear on Click-U Hierdie skyfies verskyn ook op Click-U 8 th edition / 8e uitgawe 6.7 6.0 Ses.36-