MTX221. Sessie 30 DIE KLASSIEKE TWEEDE WET VAN TERMODINAMIKA. Session 30 THE CLASSICAL SECOND LAW OF THERMODYNAMICS. Dr.

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1 Ses Sessie 30 DIE KLASSIEKE TWEEDE WET VAN TERMODINAMIKA MTX221 Hierdie skyfies verskyn ook op Click-UP 8 th edition / 8e uitgawe Session 30 THE CLASSICAL SECOND LAW OF THERMODYNAMICS Dr. Jaco Dirker These slides also appear on Click-UP

Ses. 30-2 NOT IN TEXTBOOK Nicolas Leonard Sadi Carnot (1796-1832) -French Military Engineer during the rise and fall of

-In 1824 he published first paper on reversible cycles Now called the Carnot cycle.

2 Ses NOT IN TEXTBOOK Nicolas Leonard Sadi Carnot ( ) -French Military Engineer during the rise and fall of Napoleon -Steam Engines already existed then, but were running at efficiencies of only 6%. -In 1824 he published first paper on reversible cycles Now called the Carnot cycle. - This laid the basis for the development of the 2 nd law. First recorded steam engine invented by Heron in Alexandria in the year 100. Watt Steam Engine (www-g.eng.cam.ac.uk/)

3 Ses NOT IN TEXTBOOK Watt Steam Engine (www-g.eng.cam.ac.uk/) Video: Double Acting Steam Engine

4 Ses IN TEXTBOOK If the efficiency of heat engine has to be less than 100%, what is the most efficient heat engine that can be found? Hitte-enjins Hitte-pompe Heat engines and heat pumps require two thermal reservoirs (one high temp. and one low temp. reservoir) Remember that these reservoirs have constant temperatures. Konst. temp. omkeerbaar Let s consider a cycle where every process is reversible. (thus, the cycle is also fully reversible - ie if it is a heat pump and can be reversed to become a heat engine and visa versa) Later we will show that such a cycle is the most efficient cycle. Carnot formulated such a reversible cycle. Today we call such a cycle the Carnot Cycle.

Ses. 30-5 NOT IN TEXTBOOK THE FOLLOWING SECTIONS ARE NOT IN PRESCRIBED TEXT BOOK Obtained from Thermodynamics An Engineering Approach Cengel and Boles (McGraw-Hill Publishers, 1994) Vier omkeerbare

5 Ses NOT IN TEXTBOOK THE FOLLOWING SECTIONS ARE NOT IN PRESCRIBED TEXT BOOK Obtained from Thermodynamics An Engineering Approach Cengel and Boles (McGraw-Hill Publishers, 1994) Vier omkeerbare prosesse The Carnot cycle is composed of four reversible processes. (2 isothermal and 2 adiabatic) Consider a closed system (CM) contained in a adiabatic adiabaties Piston/cylinder The insulation at the cylinder head can be removed when needed. The pressure of the surroundings is slightly less than the pressure in the cylinder. Insulation / Insulasie Can be removed Verwyderbaar

6 Ses NOT IN TEXTBOOK Reversible isothermal expansion Omkeerbare isotermiese uitesetting Insulation is removed Insulasie verwyder Brought into contact with high temp. reservoir. Both Gas and Reservoir is at T H. Gas is allowed to expand slowly (in a reversible process) Work done on surroundings. Arbeid verrig op omgewing As the gas starts to expand the temp drops by dt. Some heat flows from the reservoir to restore the temp. to T H. The temp. difference is never more than dt (thus a reversible process) Total amount of heat transferred is Q H.

Ses. 30-7 NOT IN TEXTBOOK Reversible adiabatic expansion Omkeerbare adiabatiese uitesetting Insulation is replaced and the Reservoir is removed.

7 Ses NOT IN TEXTBOOK Reversible adiabatic expansion Omkeerbare adiabatiese uitesetting Insulation is replaced and the Reservoir is removed. Due to small pressure difference the gas continues to expand slowly (in a reversible process) Work is done on the surroundings The temp. drops from T H to T L Arbeid verrig op omgewing

8 Ses NOT IN TEXTBOOK Reversible isothermal compression Omkeerbare isotermiese samedrukking Insulation is removed Brought into contact with low temp. reservoir. Both gas and reservoir is at a temp. of T L An external force slowly pushes the piston in again. Work is done on the system As gas is compressed, the temperature increases by dt. Heat is transferred to the low temp. body and temp is restored to T L. Temp difference is less than dt (thus reversible) Total heat of Q L is transferred

Ses. 30-9 NOT IN TEXTBOOK Reversible adiabatic compression Omkeerbare adiabatiese samedrukking Insulation is replaced.

9 Ses NOT IN TEXTBOOK Reversible adiabatic compression Omkeerbare adiabatiese samedrukking Insulation is replaced. Gas is compressed further (slowly via reversible process) Work is done on the system During compression the gas temp. increases again from T L to T H. The system is restored to its original state. Oorspronklike toestand

Ses. 30-10 NOT IN TEXTBOOK Summary isotermiese

10 Ses NOT IN TEXTBOOK Summary isotermiese uitsetting isothermal expansion adiabatiese uitesetting adiabatic expansion adiabatiese samedrukking adiabatic compression isotermiese samedrukking isothermal compression

Ses. 30-11 NOT IN TEXTBOOK This process can also be plotted onto a

11 Ses NOT IN TEXTBOOK This process can also be plotted onto a Pv diagram according to the state numbers used above. (1, 2, 3, and 4)

Ses. 30-12 NOT IN TEXTBOOK The area underneath line 1, 2, 3 is the work done by (or on) the system in the forward process.

12 Ses NOT IN TEXTBOOK The area underneath line 1, 2, 3 is the work done by (or on) the system in the forward process. The area underneath the line 3, 4, 1 is the work done onto (or by) the system in the reverse process. Netto arbeid The area inside the path 1,2,3,4 is the net work done by (or onto the system), depending whether it is operated as a heat engine (or a heat pump) Thus if it is operated as a heat engine more work is released during the expansion process than what was absorbed during the compression process.

13 Ses IN TEXTBOOK THIS NOW FOLLOWS FROM THE TEXT BOOK AGAIN: The Carnot cycle can also be represented similarly to a simple power plant operating between two thermal reservoirs. Carnot kringloop verteenwoordig soortgelyk aan n eenvoudige kragstasie The pump receives its work directly from the turbine. The turbine produces more work than what the pump required and thus these is a net outflow of work (positive work)

Ses. 30-14 IN TEXTBOOK Water is turned into steam in the boiler, but only by a constant infinitesimal temp. difference.

14 Ses IN TEXTBOOK Water is turned into steam in the boiler, but only by a constant infinitesimal temp. difference. Steam travels through an adiabatic turbine during a reversible process (temp is decreased). Steam is turned into water in the condenser by expelling heat to the low temp. reservoir, but only at a constant infinitesimal temp. difference. Finally the water temp is increased again by increasing the pressure within an adiabatic pump.

15 Ses IN TEXTBOOK Because all processes in the idealised Carnot cycle are reversible, the heat engine cycle can be reversed to become a refrigeration cycle. (depending on function also called a heat pump) Die Carnot krinkloop is omkeerbaar omdat alle prosesse omkeerbaar is. Dus, met omkering word n Hitte-enjin n hitte-pomp The Carnot Cycle is not dependent on the working fluid different working fluids can be used (Nitrogen, Oxygen etc.) Die Carnot krinkloop is onafhanklik van die werksvloeier.

16 Ses Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop First Proposition: A reversible Engine is the engine that has the highest efficiency while operating between two given thermal reservoirs. n Omkeerbare Enjin sal die hoogste moontlike rendement hê tussen twee gegewe termiese reservoirs. Second Proposition: All engines operating on the Carnot Cycle and which operate between the same thermal reservoirs have the same efficiency. Alle Carnot kringlope wat tussen dieselfde termiese reservoirs funksioneer sal dieselfde rendement hê. IN TEXTBOOK

Ses. 30-17 First Proposition: IN TEXTBOOK 5.

17 Ses First Proposition: IN TEXTBOOK 5.6 Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop A reversible Engine is the engine that has the highest efficiency while operating between two given thermal reservoirs. Gedagte eksperiment This proposition is proved via a thought experiment. We will make an initial assumption, which we will prove to lead to an impossible conclusion, and therefore will mean than our initial assumption was incorrect. As it appears in Textbook: Broken into steps: TH TH QH QH QH QH WI = QH - QL I R WR = QH - QL WI I WR R QL QL QL QL TL TL QH TH QH QH WI - WR I QL WR R QL WI - WR I QL WR R QL TL TL QL - QL TL QL - QL

18 Ses NOTIN TEXTBOOK 5.6 Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop First Proposition: 1 T H 1 Consider an irreversible (I) heat Q H Q H engine that has a higher efficiency than a reversible (R) engine at the I R same thermal reservoirs (this is our W I = Q H - Q L assumption) Aaname: Onomkeerbare enjin het n hoër rendement as n omkeerbare enjin by dieselfde termiese reservoirs Q L T L Q L W R = Q H - Q L Both exchange Q H heat with the high temp. reservoir. Because the Irreversible heat engine is more efficient than the reversible one, the irreversible work output is more than that of the reversible This means than Q L (irreversible) is less than Q L (reversible)

19 Ses Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop 1 First Proposition: 2 Reversible Heat Engine is reversed to become a Heat Pump with its original efficiency when it was a heat engine 2 Keer omkeerbare hitte-enjin om in n Hittepomp (behou oorspronklike rendement) Q H T H NOTIN TEXTBOOK Q H W I I W R R Q L Q L T L 3 4 5

20 Ses Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop 1 First Proposition: 3 Because the Irreversible Engine produced more power than the reversible cycle, A portion of the irreversible engine power output is 2 used to drive the reversible heat pump. And there are excess work Gebruik uitset van onomkeerbare hitte-enjin om die omkeerbare hitte-pomp aan te dryf. Oorblywende arbeid is nog beskikbaar 3 W I - W R I Q H Q L T H W R NOTIN TEXTBOOK R Q H Q L T L 4 5

21 Ses Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop 1 First Proposition: 4 Both Cycles exchange the same amount of heat with the high temp. reservoir Thus this reservoir can be by-passed. 2 Elimineer hoë temp. hitte reservoir aangesien geen netto hitte-oordag plaasvind nie 3 NOTIN TEXTBOOK 4 Q H W I - W R I Q L W R R Q L T L 5

22 Ses Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop 1 First Proposition: 5 The remaining equipment is combined into a single cycle which only exchanges heat with the low temp. reservoir. 2 Oortreding van Kelvin Planck Stelling This contradicts the Kelvin Planck statement, which means our original assumption is invalid. THUS: A reversible cycle (consisting of reversible processes) is the most efficient cycle. END OF PROOF Aanvanklike aaname foutief 3 4 NOTIN TEXTBOOK THE CARNOT CYCLE IS A REVERSIBLE CYCLE AND WILL BE USED TO CALCULATE THE HIGHEST EFFICIENCY A HEAT ENGINE MAY HAVE. 5 Q L - Q L Q L - Q L T L

23 Ses Second Proposition: All engines operating on the Carnot Cycle and which operate between the same thermal reservoirs have the same efficiency IN TEXTBOOK 5.6 Two Propositions Regarding Efficiency of a Carnot Cycle Twee proposisies aangaande die Rendement van n Carnot Kringloop Can be proved using same approach used for the first proposition

24 Ses Termodinamiese Temperatuurskaal 5.7 Thermodynamic Temperature Scale The 0 th Law gives the foundation of temp. measurement in terms of temperature equivalence. To develop a temp. scale we can construct a master thermometer operating with a particular substance, which all other temperatures can be compared with. If however a temp. scale can be obtained that is independent of the substance, it would be desirable. Such a scale is called an ABSOLUTE SCALE. Termometer wat onafhanklik is van stof is gerieflik, staan bekend as n ABSOLUTE SKAAL. IN TEXTBOOK

25 Ses Termodinamiese Temperatuurskaal 5.7 Thermodynamic Temperature Scale Onafhanklik van werksvloeier The Carnot Heat Engine Cycle efficiency is independent of the working fluid and only dependent on the Thermal reservoir temperatures. Thus: thermal Q L 1 1 QH T L, T H IN TEXTBOOK Many functions exist to satisfy ψ. The simplest: Q Q L H T T L H This means: that the Carnot Heat Engine Cycle efficiency is: Carnot Hitte-Enjin Kringloop Rendement TL thermal 1 T H This is the highest efficiency that any heat engine can achieve in an ideal word.

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

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