1 Reversible Processes The second law of thermodynamics state that no heat engine can have an efficiency of 100%. Then one may ask, what is the highest efficiency that a heat engine can possibly have. Before we answer this question, we need to define an idealized process first, which is called the reversible process. The processes discussed earlier occurred in a certain direction. They can not reverse themselves irreversible processes.

2 Reversible Processes A reversible process is defined as a process that can be reversed without leaving any trace on either system or surroundings. This is possible if the net of heat and net work exchange between the system and the surrounding is zero for the combined process (original and reverse). Quasi- equilibrium expansion or compression of a gas

3 Reversible processes actually do not occur in nature. They are simply idealization of actual processes. Reversible processes can never be achieved. You may be wondering, then, why we are bothering with such fictitious processes: 1. Easy to analyze 1. Serve as idealized model

4 Engineers are interested in reversible processes because: when Reversible processes are approximated instead of the Actual ones 1. Work-producing devices such as car engine and gas or steam turbine deliver the most work, and 2. Work-consuming devices such as compressors, fan, and pumps consume the least work.

5 Reversible processes can be viewed as theoretical limits for the corresponding not reversible ones. We may never be able to have a reversible process, but we may certainly approach it. The more closely we approximate a reversible process, the more work delivered by a work- producing device or the less work required by a work-consuming device. Processes that are not reversible are called Irreversible processes.

6 Reversible processes Ideal processes Irreversible processes Actual processes

7 Irreversible Process If the process leaves any trace on either system or surroundings, then it is an irreversible. The factors that cause a process to be irreversible are called irreversibilities. They include:

8 1- Friction Work is done to raise the block and overcome friction. Block is getting hotter due to friction. In the reverse process, the block is getting even hotter due to friction. Heat should be rejected to the surrounding to bring it back to its initial position. Hence, irreversible process.

9 2- Unrestrained expansion Unrestrained expansion means W=0 To bring the gas back to its initial pressure and Temperature, work must be supplied by surrounding. Hence irreversible process.

10 3- Mixing of two gases, Work should be supplied from the surrounding to separate the two gases. Hence, irreversible process.

11 4- Heat transfer through a finite temperature difference 1. A system at a high temperature body and a low temperature body, let heat be transferred from T H to T L ( no work will be involved). 2. The only way to bring the system back to T L is to cool it by refrigerator. 3. The refrigerator requires work from the surrounding W input. 4. The net effect is extra heat rejected to the surrounding equal in magnitude to the work. 5. Hence it is an irreversible process. Ref Q W Q High Temperature Low Temperature

12 6. Since the surrounding is permanently affected, heat transfer through a finite temperature difference is an irreversible process. 7. The smaller the temp difference the smaller the irreversibility. 8. As  T approaches zero, the process can be reversed in direction (at least theoretically) without requiring any refrigeration. 9. This is a conceptual process and can not be done in real world.

13 Internally and Externally Reversible Process A process is called internally reversible if no irreversibility occur within the boundaries of the system during the process. A process is called externally reversible if no irreversibility occur outside the system boundaries during the process. A process is called totally reversible or simply reversible if it involves no irreversibility within the system or its surroundings during the process. External reversible External irreversible

14 Heat transfer process and finite temperature difference process 1. For a Heat transfer process to be revisable process it has to be an Isothermal process. 2. For a finite temperature difference process to be revisable process it has to be an adiabatic process.

15 Cycles that are composed of reversible processes will give the maximum net work and consumes the minimum work. One of these cycles is the Carnot Cycle. Named for French engineer Nicolas Sadi Carnot ( ) It is composed of four processes as follows:

16 Process 1-2: A reversible isothermal expansion The gas is allowed to expand isothermally by receiving heat ( Q H ) from a hot reservoir.

17 Process 2-3: A reversible adiabatic expansion The cylinder now is insulated and the gas is allowed to expand adiabatically and thus doing work on the surrounding. The gas temperature decreases from T H to T L.

18 Process 3-4: A reversible isothermal compression The insulation is removed and the gas is compressed isothermally by rejecting heat (Q L ) to a cold reservoir.

19 Process 4-1: A reversible adiabatic compression The cylinder is insulated again and the gas is compressed adiabatically to state 1, raising its temperature from T L to T H

20 Net work done by Carnot cycle is the area enclosed by all process The Carnot cycle is the most efficient cycle operation between two specified temperatures limits.

21 Carnot cycle can be executed in many different ways (notice the direction of the cycle) all Processes are reversible

22 Reversed Carnot Cycle Process 2-3: The gas expands isothermally at T L while receiving Q L from the cold reservoir. Process 3-4: The gas is compressed adiabatically raising its temperature to T H. Process 4-1: The gas is compressed isothermally by rejecting Q H to the hot reservoir. Process 1-2: The gas expands adiabatically (throttling valve) reducing its temp from T H to T L.

23 Reversed Carnot Cycle All Processes are reversible

24 Carnot principles 1.No heat engine is more efficient than a reversible one operating between the same two reservoirs. 2.The thermal efficiencies of all reversible heat engines operating between the same two reservoirs are the same ( same T H and T L will have same Efficiency). Low temperature reservoir at T L

25 The Thermodynamic Temperature Scale A temperature scale that is independent of the properties of the substances that are used to measure temperature is called a thermodynamic temperature scale. That is the Kelvin scale, and the temperatures on this scale are called absolute temperatures. The second Carnot principle state that the thermal efficiencies of all reversible heat engines operating between the same two reservoirs are the same.  th, rev = f (T H,T L )

26 Efficiency of a Carnot Engine For a reversible cycle the amount of heat transferred is proportional to the temperature of the reservoir. Only true for the reversible case T must be in o K

27 COP of a Reversible Heat Pump and a Reversible Refrigerator Only true for the reversible case

28 How do Reversible Carnot Heat Engine compare with real engines?

29 No heat engine can have a higher efficiency than a reversible heat engine operating between the same high- and low-temperature reservoirs.

30 COP of Carnot Refrigerator How do Carnot Refrigerator compare with real Refrigerator? COP of Refrigerator

31 COP of Carnot Heat PumpCOP of real Heat Pump How do Carnot Heat Pump compare with real one?

32 No refrigerator can have a higher COP than a reversible refrigerator operating between the same temperature limits.

33 How to increase the efficiency of a real heat engine? 1- Increase T H but you are limited with melting temperature of the engine material. 2- Decrease T L but you are limited with your environment or ambient condition.

34 EXAMPLE 6–5 Analysis of a Carnot Heat Engine A Carnot heat engine, receives 500 kJ of heat per cycle from a high-temperature source at 652°C and rejects heat to a low- temperature sink at 30°C. Determine (a) the thermal efficiency of this Carnot engine and (b) the amount of heat rejected to the sink per cycle. Carnot Engine Carnot Heat pump Reversible heat engine The maximum efficiency All Refer to Same cycle (Carnot)

35 EXAMPLE 6–5 Analysis of a Carnot Heat Engine (a) The Carnot heat engine is a reversible heat engine, and so its efficiency can be determined from Eq. 6–18 to be That is, this Carnot heat engine converts 67.2 percent of the heat it receives to work. (b) The amount of heat rejected QL by this reversible heat engine is easily determined from Eq. 6–16 to be

36 The Quality of Energy The fraction of heat that can be converted to work as a function of source temperature (for constant Sink temperature ofT L = 303 K).

37 The Quality of Energy The higher the temperature of the thermal energy, the higher its quality.

38 Quantity versus Quality in Daily Life The quantity of energy is already conserved. What is not conserved is the quality of energy, or the work potential of energy. Wasting energy is synonymous to converting it to a less useful form. One unit of high-quality energy can be more valuable than three units of lower-quality energy. For example, a finite amount of thermal energy at high temperature is more attractive to power plant engineers than a vast amount of thermal energy at low temperature, such as the energy stored in the upper layers of the oceans at tropical climates. Quantity alone cannot give the whole picture, and we need to consider quality as well. When evaluating something we need to look at something from both the first- and second-law points of view

39 EXAMPLE 6–6 A Questionable Claim for a Refrigerator An inventor claims to have developed a refrigerator that maintains the refrigerated space at 35°F (2 °C) while operating in a room where the temperature is 75°F ( 24 °C )and that has a COP of Is this claim reasonable? Note: always use the absolute Temperature scale (R or K) the claim is false 12.4 is the max. how he is going to get 13.5 !!!!

40 Example (6-7): Heating a House by a Carnot Heat Pump A heat pump is to be used to heat a house during the winter, as shown in the figure at right. The house is to be maintained at 21 o C at all times. The house is estimated to be losing heat at a rate of 135,000 kJ/h when the outside temperature drops to - 5 o C. Determine the minimum power required to drive this heat pump. Sol:

41 The heat pump must supply heat to the house at a rate of Q H = 135,000 kJ/h = 37.5 kW. The power requirements are minimum when a reversible heat pump is used to do the job. The COP of a reversible heat pump operating between the house and the outside air is Then the required power input to this reversible heat pump becomes

42 Example (1)

43

44 Example (2) Direction is correct for the HE, the Sink, source and Wnet are exist : the second law is satisfies B) Is violating the 2 st Law ; QL = 0 impossible C) Is violating the 1 st Law

45 Example (3)

46 Example (3)- CONTINUE W = Q H1 -Q L1 = Q H1 (1- Q L1 /Q H1 )  W = Q H1 (1-T O /T H ) also W = Q H2 -Q L2 = Q L2 (Q H2 /Q L2 -1))  W = Q L2 (T O /T L -1)