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

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1 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

2 Ses.36- Entropieverandering van n Ideale Gas 6.7 Entropy Change of an Ideal Gas Isentropiese proses Isentropic rocess of an IDEAL gas. Consider an ideal Gas undergoing an isentropic process. (thus entropy is constant): s s 0 Ideale gas C C po po d d R ln R ln isentropies DO EX6.6 (Ed 8) YOURSELF DOEN VB6.6 (Uitg.8) SELF

3 Ses.36-3 Entropieverandering van n Ideale Gas 6.7 Entropy Change of an Ideal Gas Isentropiese proses Isentropic rocess of an IDEAL gas. konstante Spesifieke Hitte As a special case consider a constant Specific Heat: Resulting in: his is written as: However: Or as: R C 0 C p C po ln ln 0 C C 0 R C R ln 0 v0 ln R C 0 k k 0 C p0 (where k also listed in A5) C v0

4 Ses.36-4 Entropieverandering van n Ideale Gas 6.7 Entropy Change of an Ideal Gas Isentropiese proses Isentropic rocess of an IDEAL gas. herefore k k v R Combining this with the following can also be written: v v v v k k ** ** ** k k v v ** hese equations do appear on our formulae sheet. his last expression results in: v k const Since we are dealing with control mass (constant mass) this is thus a special case of a olytropic process. Only for constant spec. heat olitropiese proses

5 Ses.36-5 Omkeerbare olitropiese roses vir n Ideale Gas 6.8 Reversible olytropic rocess for an Ideal Gas olitropiese proses Let s Re-look politropic processes, but now only focus on ideal gasses olitropic processes appear as straight lines on a Log -Log V diagram Ideale gas his means: d ln d lnv n Rewritten as: d ln nd lnv 0 For a straight line n = const, for which after integration the following known expression is obtained: n n n V const V V Ses. 53-5

6 Ses Reversible olytropic rocess for an Ideal Gas Omkeerbare olitropiese roses vir n Ideale Gas As we saw before, for an ideal gas the following can be written: n v v n n n v v Refer to earlier slide

7 Ses.36-7 Omkeerbare olitropiese roses vir n Ideale Gas 6.8 Reversible olytropic rocess for an Ideal Gas Let s consider some types of processes: (plotted on v and s diagrams) V n const Isobaric ( = const.) n =0 Isothermal ( = const)* n = Isentropic (s = const)* + n = k Isochoric (v = const) n = * ONLY FOR IDEAL GAS + ONLY FOR CONS C p Boundary moving work given by: W V V n (if n ) For an ideal gas becomes: W mr n Ses. 53-7

8 Ses.36-8 Omkeerbare olitropiese roses vir n Ideale Gas 6.8 Reversible olytropic rocess for an Ideal Gas Reversible Isothermal rocess For an isothermal process, (n = ), boundary moving work is given by : W V ln V ln V For an ideal gas this becomes: V V W mr ln mr ln V Because is const, there is no change in the internal Energy (Ideal Gas) herefore heat transfer is equal to work: hus From st Law: From nd Law: Dus, hitte-oordrag en arbeid is gelyk q u w ds v q w dv v ln v q Omkeerbare Isotermiese roses du dv Ses. 53-8

9 Ses.36-9 Alegemene Herindering General Reminder Remember: For a (internally) Reversible rocess, the following may be said: Onthou, Vir n (interne) Omkeerbare roses, kan die volgende gesê word:

10 Ses.36-0 Entropie verandering vir n KM tydens n Onomkeerbare roses 6.9 Entropy Change of a CM during an Irreversible rocess We know what happens in Reversible Cycles and rocesses What about Irreversible Cycles and rocesses? Consider cycles: AB is omkeerbaar Cycle AB is reversible (both A and B are reversible processes) Cycle CB is irreversible (C is an irreversible process) CB is onomkeerbaar What happens to the entropy in an irreversible process?

11 Ses.36- Entropie verandering vir n KM tydens n Onomkeerbare roses 6.9 Entropy Change of a CM during an Irreversible rocess We found that: S S Q his is a very important equation - it forms the basis of many further concepts. What does this mean? Vir enige onomkeerbare proses, is die verdandering van entropie altyd meer positief as vir n omkeerbare proses. Intern omkeerbare proses hus for an INERNALLY reversible process: onomkeerbaar For an irreversible process: S his is true for Q >0, Q = 0, and Q<0 For any irreversible process, the change in entropy is always more positive than for a reversible process. S Q * S S Q * * lease note: this is the entropy of the system, and not yet that Ses. of 53- the surroundings

12 Ses.36- Entropie verwekking en die entropie vgl. 6.0 Entropy Generation and the Entropy Eq. Q We now know that: ds he following can thus be written: Where the entropy generation must be greater than zero: Entropie verwekking Q ds S gen S gen 0 he entropy generation is caused by factors such as friction, unconstrained expansion etc External irreversibilities such as heat transfer over a finite temp. difference also causes entropy generation. Entropie verwekking is weens faktore soos wrywing, onheheerde uitsetting ens Eksterne onomkeerbaarhede soos hitte-oordrag oor n eindige temp. verskil veroorsaak ook entropie verwekking. Important Note (not in textbook) Q Entropy transfer only occurs with Heat transfer ds S gen Work is thus entropy-free However, the processes involved with work may cause entropy generation. Entropie oordrag geskied net met hitte-oordrag nie met arbeid nie, maar entropie mag verwek word tydens die prosesse verwant aan arbeid.. Ses. 53-

13 Ses Entropy Generation and the Entropy Eq. For reversible processes: 0 S gen omkeerbaar Q ds W dv Entropie verwekking en die entropie vgl. onomkeerbaar Q ds For irreversible processes: 0 S gen Q W ds irr S gen dv irr S gen * S gen * his is from the st Law: Q du irr W irr and the Gibbs equation: ds du dv We thus see that the heat transfer and work in a irreversible process is less than in a reversible process. he missing work can be seen as a lost opportunity to extract work. hus in general: Q S S S gen Hitte-oordrag arbeid

14 Ses Entropy Generation and the Entropy Eq. Entropie-balans From this an entropy balance can be obtained: Entropie verwekking en die entropie vgl. Q ds S gen Entropy = +in out +gen Entropie kan geskep word, maar nie vernietig word nie Entropy can thus be created but not destroyed his is in contrast with energy which can not be created

15 Ses.36-5 Entropie verwekking en die entropie vgl. 6.0 Entropy Generation and the Entropy Eq. Important Conclusions: oename / Afname in Entropie. Increase / Decrease of Entropy: Entropy increases by: heat flow in and irreversible processes Entropy of a system decreases by: heat flow out. Adiabatiese roses. Adiabatic rocesses: For irreversible adiabatic processes the increase in S is due to irreversibilites

16 Ses.36-6 Entropie verwekking en die entropie vgl. 6.0 Entropy Generation and the Entropy Eq. Important Conclusions: Arbeid 3. Work: Irreversibilities result in less work Stelsel teenoor omgewing 4. System vs Environment Consider heat transfer from Environment to System System experiences a increase in entropy due to heat flow in Environment experiences a decrease in entropy due to loss of heat he entropy that the system gains is not equal to the entropy the environment looses But the overall entropy will thus change due to irreversibilities.

17 Ses.36-7 Arbeid en Hitte vir omkeerbare en onomkeerbare prosesse Entropie verwekking en die entropie vgl. 6.0 Entropy Generation and the Entropy Eq. Work and Heat for reversible and irreversible processes. Reversible processes drawn with solid line Irreversible processes drawn with dashed line. Irreversible Onomkeerbaar Reversible Omkeerbaar