Thermodynamics Third Law Heat Engines

Transcription

1 Thermodynamics Third Law Heat Engines Lana Sheridan De Anza College May 11, 2018

2 Last time heat engines heat pumps Carnot engines

3 Overview efficiency of Carnot engines the Third Law real engines

4 Heat Engine Recap Steam engines and later incarnations of the engine run on a very simple principle: heat is transferred from a hot object to a colder object and mechanical work is done in the process. Heat engines run in a cycle, returning their working fluid back to its initial state at the end of the cycle. In practice, usually some chemical energy (burning fuel) is used to raise the temperature of one object, and the colder object remains at the ambient temperature.

5 The Carnot Cycle P A The work done during the cycle equals the area enclosed by the path on the PV diagram. Q h B W eng Figure PV diagram for the D Q c C T h T c V and the PV dia of two adiabati 1. Process The gas ture T h. ervoir th piston. 2. In proce thermal energy e peratur raising t 3. In proce energy r peratur and the

6 Maximum Efficiency of an Engine This means e > e C W Q h > W Q hc Q h < Q hc We also know that W = Q h Q c (energy conservation). Since the works are equal: W = W c Q h Q c = Q hc Q cc Rearranging: Q hc Q h = Q cc Q c But the LHS is positive if e > e C. Heat arrives at the hot reservoir and leaves the cold one! Violates the Second Law.

7 Maximum Efficiency of an Engine Putting the imagined engine and the Carnot heat pump together: Hot reservoir at T h Q hc Q h > 0 Q cc Q c > 0 Q h Heat engine Q c W Cold reservoir at T c Q hc W C Carnot heat pump Q c C Q h,net Figure 22.9 A Carnot engine operated as a heat pump and another engine with a propose Q higher efficiency c,net operate betwe two energy reservoirs. The work output and input are matched. Violates maximum the Second possible Law. efficiency for real engines. Let us confirm that engine is the most efficient. We imagine a hypothetical engine with a greater than that of the Carnot engine. Consider Figure 22.9, whic

8 Carnot s Theorem Carnot s Theorem No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. But how efficient is a Carnot engine?

9 The Carnot Cycle P A The work done during the cycle equals the area enclosed by the path on the PV diagram. Q h B W eng Figure PV diagram for the D Q c C T h T c V and the PV dia of two adiabati 1. Process The gas ture T h. ervoir th piston. 2. In proce thermal energy e peratur raising t 3. In proce energy r peratur and the

10 Efficiency of a Carnot Engine First, we can relate the volumes at different parts of the cycle. In the first adiabatic process: T h V γ 1 B In the second adiabatic process: T h V γ 1 A = T c V γ 1 C = T c V γ 1 D Taking a ratio, then the γ 1 root: V B V A = V C V D

11 Efficiency of a Carnot Engine First law: E int = Q + W = 0 gives for the first isothermal process ( ) VB Q h = nrt h ln Second isothermal process: Q c = nrt c ln V A ( VC V D ) We will take a ratio of these to find the efficiency. Noting that = V C V D : V B V A Q c Q h = T c T h

12 Efficiency of a Carnot Engine Recall, efficiency of a heat engine: e = 1 Q c Q h Efficiency of a Carnot engine: e = T h T c T h = 1 T c T h (T is measured in Kelvin!) This is the most efficient that any heat engine operating between two reservoirs at constant temperatures can be.

13 Third Law of Thermodynamics 3rd Law As the temperature of a material approaches zero, the entropy approaches a constant value. The constant value the entropy takes is very small. It is actually zero if the lowest energy state of the material is unique. Another way to express the third law: 3rd Law - alternate It is impossible to reach absolute zero using any procedure and only a finite number of steps.

14 Entropy in the Carnot Cycle Since the working fluid returns to its initial state along reversible paths, the change in the entropy for the whole cycle is

15 Entropy in the Carnot Cycle Since the working fluid returns to its initial state along reversible paths, the change in the entropy for the whole cycle is S = 0.

16 Entropy in the Carnot Cycle Since the working fluid returns to its initial state along reversible paths, the change in the entropy for the whole cycle is S = 0. We can see this from an analysis also: 1 S = T dq r In the reversible adiabatic processes S = 0. In the reversible isothermal portions, T is constant so S = Q T. For the cycle S = Q h T h Q c T c

17 Entropy in the Carnot Cycle For the cycle S = Q h T h Q c T c We just found that So Q h Q c = T h T c Q h T h = Q c T c And for the cycle S = 0

18 Entropy in the Carnot Cycle We can represent the Carnot Cycle on a TS diagram: Temperature T a d Q H Q L Entropy S Fig The Carnot cycle of b c T H T L it is is do area Figs. quan perf invo Carn tere gram isoth cycle stan ing t

19 Heat Engine question Consider and ocean thermal energy conversion (OTEC) power plant that operates on a temperature difference between deep 4 C water and 25 C surface water. Show that the Carnot (ideal) efficiency of this plant would be about 7%. 0 Hewitt, page 331, problem 2.

20 In a gasoline engine, six processes occur in each cycle; they are illustrated in Figure In this discussion, let s consider the interior of the cylinder above the piston to be the system that is taken through repeated cycles in the engine s operation. For a given cycle, the piston moves up and down twice, which represents a four-stroke cycle consisting of two upstrokes and two downstrokes. The processes in the cycle Car Engines Car can be engines approximated work by the Otto by cycle burning shown in fuel the PV indiagram cylinders Figure with pistons. (page 666). In the following discussion, refer to Figure for the pictorial representation of the strokes and Figure for the significance on the PV diagram of the letter designations below: The four stroke cycle: 1. During the intake stroke (Fig a and O S A in Figure 22.13), the piston moves downward and a gaseous mixture of air and fuel is drawn into the The intake valve opens, and the air fuel mixture enters as the piston moves down. The piston moves up and compresses the mixture. The spark plug fires and ignites the mixture. The hot gas pushes the piston downward. The exhaust valve opens, and the residual gas escapes. The piston moves up and pushes the remaining gas out. Spark plug Air and fuel Exhaust Piston Intake Compression Spark Power Release Exhaust a b c d e f Figure The four-stroke cycle of a conventional gasoline engine. The arrows on the piston indicate the direction of its motion during each process.

21 Car Engines Air and fuel The intake valve opens, and the air fuel mixture enters as the piston moves down. Spark plug Piston Intake

22 b Car Engines The piston moves up and compresses the mixture. g n Compression

23 s downward and a gaseous mixture of air and fuel is drawn into the Car Engines alve the air enters moves Spark plug The piston moves up and compresses the mixture. The spark plug fires and ignites the mixture. The hot gas pushes the piston downward. The exha opens, an residual g Piston e Compression Spark Power Relea

24 gaseous mixture of air and fuel is drawn into the Car Engines n moves ompresses ure. The spark plug fires and ignites the mixture. The hot gas pushes the piston downward. The exhaust valve opens, and the residual gas escapes. The pis up and remain ssion Spark Power Release Exha

25 e of air and fuel is drawn into the Car Engines spark plug and ignites ixture. The hot gas pushes the piston downward. The exhaust valve opens, and the residual gas escapes. The piston moves up and pushes the remaining gas out. Exhaust Spark Power Release Exhaust c d e f

26 2.13), the piston rawn into the Car Engines t gas the piston ard. The exhaust valve opens, and the residual gas escapes. The piston moves up and pushes the remaining gas out. Exhaust ower Release Exhaust d e f

27 Car Engines and the Otto Cycle 666 Chapter 22 Heat Engines, Entro The Otto cycle approximates the real 4-stroke cycle we just discussed. P T A Q h B T C O C Adiabatic processes V 2 V 1 Figure PV diagram for D A Q c V cylind energ as pot from sion s from 2. Durin ton m volum work area u 3. Comb 22.13)

28 Car Engines and the Otto Cycle The efficiency of the Otto cycle is e = 1 1 (V 1 /V 2 ) (γ 1) (See example 22.5 for a proof of this expression.) A typical value for the volume compression is V 1 /V 2 = 8, which would give an efficiency of 56%. Real efficiencies of car engines are much less than this, 20%. There is heat loss, work lost overcoming friction, and imperfect combustion.

29 In this discussion, let s consider the interior of the cylinder above the piston to be the system that is taken through repeated cycles in the engine s operation. For a given cycle, the piston moves up and down twice, which represents a four-stroke Car Engines cycle consisting of two upstrokes and two downstrokes. The processes in the cycle can be approximated by the Otto cycle shown in the PV diagram in Figure (page 666). In the following discussion, refer to Figure for the pictorial representation of the strokes and Figure for the significance on the PV diagram of the letter designations below: The four stroke cycle: 1. During the intake stroke (Fig a and O S A in Figure 22.13), the piston moves downward and a gaseous mixture of air and fuel is drawn into the The intake valve opens, and the air fuel mixture enters as the piston moves down. The piston moves up and compresses the mixture. The spark plug fires and ignites the mixture. The hot gas pushes the piston downward. The exhaust valve opens, and the residual gas escapes. The piston moves up and pushes the remaining gas out. Spark plug Air and fuel Exhaust Piston Intake Compression Spark Power Release Exhaust a b c d e f Figure The four-stroke cycle of a conventional gasoline engine. The arrows on the piston indicate the direction of its motion during each process.

30 Jet Engines Jet engines are even simpler and more efficient than car engines. However, they require more advanced materials... 1 Turbofan schematic from Wikipedia by K. Aainsqatsi.

31 Advanced Jets: Scramjet...and higher speeds of operation. 1 Scramjet schematic from Wikipedia by User:Emoscopes.

32 Summary Carnot engines real engines Thermodynamics Test Monday, May 14. Homework Serway & Jewett: Ch 22, OQs: 1, 3, 7; CQs: 1; Probs: 1, 3, 9, 15, 20, 23, 29, 37, 67, 73, 81