1. Chapter 11 The Second Law of Thermodynamics

2. The second law of thermodynamics states that processes occur in a certain direction, not in just any direction. Physical processes in nature can proceed toward equilibrium spontaneously:
Water flows down a waterfall.
Gases expand from a high pressure to a low pressure.
Heat flows from a high temperature to a low temperature.
Once it has taken place, a spontaneous process can be reversed, but it will not reverse itself spontaneously. Some external inputs energy, must be expended to reverse the process. Consider a paddle wheel mechanism that is operated by the fall of a mass. The paddle wheel rotates as the mass falls and stirs a fluid within an insulated container. As a result, the potential energy of the mass decreases, and the internal energy of the fluid increase in accordance with the conservation of energy principle. However, the reverse process, raising the mass by transferring heat from the fluid to the paddle wheel, does not occur in nature, although doing so would not violate the first law of thermodynamics. Spontaneous processes can proceed only in a particular direction. The first law of thermodynamics gives no information about direction; it states only that when one form of energy is converted into another, identical quantities of energy are involved regardless of the feasibility of the process. We know by experience that heat flows spontaneously from a high temperature to a low temperature. But heat flowing from a low temperature to a higher temperature with no expenditure of energy to cause the process to take place would not violate the first law.

3. Transferring heat to a paddle wheel will not cause it to rotate.
This process cannot occur even though they are not in violation of the first law.

4. The first law is concerned with the conversion of energy from one form to another. Joule's experiments showed that energy in the form of heat could not be completely converted into work; however, work energy can be completely converted into heat energy. Evidently heat and work are not completely interchangeable forms of energy. Furthermore, when energy is transferred from one form to another, there is often a degradation of the supplied energy into a less “useful” form. We shall see that it is the second law of thermodynamics that controls the direction processes may take and how much heat is converted into work. A process will not occur unless it satisfies both the first and the second laws of thermodynamics.
Heat (thermal) reservoir
A heat reservoir is a sufficiently large system in stable equilibrium to which and from which finite amounts of heat can be transferred without any change in its temperature.

5. Bodies with relatively large thermal masses can be modeled as thermal energy reservoirs.
In practice, large bodies of water such as oceans, lakes, and rivers as well as the atmospheric air can be modeled accurately as thermal energy reservoirs because of their large thermal energy storage capabilities or thermal masses.
The atmosphere, for example, does not warm up as a result of heat losses from residential buildings in winter. Likewise, megajoule of waste energy dumped in large rivers by power plants do not cause any significant change in water temperature

6. A high temperature heat reservoir from which heat is transferred is sometimes called a heat source. A low temperature heat reservoir to which heat is transferred is sometimes called a heat sink.
A source supplies energy in the form of heat, and a sink absorbs it.
Heat Engine
Work can always be converted to heat directly and completely, but the reverse is not true. Converting heat to work requires the use of some special devices. These devices are called heat engines.

7. The devices that convert heat to work.
They receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.).
They convert part of this heat to work (usually in the form of a rotating shaft.)
They reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.).
They operate on a cycle.
Heat engines and other cyclic devices usually involve a fluid to and from which heat is transferred while undergoing a cycle. This fluid is called the working fluid.
Part of the heat received by a heat engine is converted to work, while the rest is rejected to a sink.

8. A heat engine is a thermodynamic system operating in a thermodynamic cycle to which net heat is transferred and from which net work is delivered.
The system, or working fluid, undergoes a series of processes that constitute the heat engine cycle.
The following figure illustrates a steam power plant as a heat engine operating in a thermodynamic cycle.

9. A portion of the work output of a heat engine is consumed internally to maintain continuous operation.
Thermal Efficiency,
The thermal efficiency is the index of performance of a work-producing device or a heat engine and is defined by the ratio of the net work output (the desired result) to the heat input (the costs to obtain the desired result).
For a heat engine the desired result is the net work done and the input is the heat supplied to make the cycle operate. The thermal efficiency is always less than 1 or less than 100 percent.

10. Now apply the first law to the cyclic heat engine.
where
Here the use of the in and out subscripts means to use the magnitude (take the positive value) of either the work or heat transfer and let the minus sign in the net expression take care of the direction.
Now apply the first law to the cyclic heat engine.
0 (Cyclic)
The cycle thermal efficiency may be written as

11. Cyclic devices such as heat engines, refrigerators, and heat pumps often operate between a high-temperature reservoir at temperature TH and a low-temperature reservoir at temperature TL.

12. The thermal efficiency of the above device becomes
Example 11-1
A steam power plant produces 50 MW of net work while burning fuel to produce 150 MW of heat energy at the high temperature. Determine the cycle thermal efficiency and the heat rejected by the cycle to the surroundings.

13. Example 11-2
An automobile engine produce 136 hp on the output shaft with a thermal efficiency of 30%. The fuel it burns gives kJ/kg as energy release. Find the total rate of energy rejected to the ambient and the rate of fuel consumption in kg/s
Solution
From the definition of heat engine efficiency and the conversion of hp we have
The energy equation for the overall engine gives
From the energy release in the burning we have , so

14. Even the most efficient heat engines reject almost one half of the energy they receive as waste heat.

15. 7-19
A heat engine that pumps water out of an underground mine accepts 500 kJ of heat and produces 200 kJ of work. How much heat does it reject, in kJ? [300 kJ]
7-20
A heat with a thermal efficiency of 40 percent rejects 1000 kJ/kg of heat. How much heat does it receive? [1667 kJ/kg]

16. Heat Pump
A heat pump is a thermodynamic system operating in a thermodynamic cycle that removes heat from a low-temperature body and delivers heat to a high-temperature body. To accomplish this energy transfer, the heat pump receives external energy in the form of work or heat from the surroundings.
While the name “heat pump” is the thermodynamic term used to describe a cyclic device that allows the transfer of heat energy from a low temperature to a higher temperature, we use the terms “refrigerator” and “heat pump” to apply to particular devices. Here a refrigerator is a device that operates on a thermodynamic cycle and extracts heat from a low-temperature medium. The heat pump also operates on a thermodynamic cycle but rejects heat to the high-temperature medium.
The following figure illustrates a refrigerator as a heat pump operating in a thermodynamic cycle.

17. Coefficient of Performance, COP
In a household refrigerator, the coils usually behind the refrigerator where heat is dissipated to the kitchen air serve as the condenser
A capillary tube where the refrigerant’s temperature and pressure drop drastically due to the throttling effect.
The refrigerant enters the compressor as a vapour and is compressed to the condenser pressure
In a household refrigerator, the freezer compartment where heat is absorbed by the refrigerant serves as the evaporator.
Coefficient of Performance, COP
The index of performance of a refrigerator or heat pump is expressed in terms of the coefficient of performance, COP, the ratio of desired result to input. This measure of performance may be larger than 1, and we want the COP to be as large as possible.

18. For the heat pump acting like a refrigerator or an air conditioner, the primary function of the device is the transfer of heat from the low- temperature system.
The objective of a refrigerator is to remove heat QL from the refrigerated space.
For the refrigerator the desired result is the heat removal at the low temperature and the input is the net work into the device to make the cycle operate.

19. Now apply the first law to the cyclic refrigerator.
and the coefficient of performance becomes

20. For the device acting like a “heat pump,” the primary function of the device is the transfer of heat to the high-temperature system. The coefficient of performance for a heat pump is
Note, under the same operating conditions the COPHP and COPR are related by

21. When installed backward, an air conditioner functions as a heat pump.

22. Example 11-3
The COP and the refrigeration rate of a refrigerator are given. The power consumption and the rate of heat rejection are to be determined.
Assumptions The refrigerator operates steadily.
Analysis (a) Using the definition of the coefficient of performance, the power input to the refrigerator is determined to be
(b) The heat transfer rate to the kitchen air is determined from the energy balance,
cool space
Kitchen air R
COP=1.2
60 kJ/min

23. Second Law Statements
The following two statements of the second law of thermodynamics are based on the definitions of the heat engines and heat pumps.
Kelvin-Planck statement of the second law
It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.
The Kelvin-Planck statement of the second law of thermodynamics states that no heat engine can produce a net amount of work while exchanging heat with a single reservoir only. In other words, the maximum possible efficiency is less than 100 percent.

24. Clausius statement of the second law
< 100%
The Kelvin-Planck statement can also be expressed as no heat engine can have a thermal efficiency of 100 percent, or as for a power plant to operate, the working fluid must exchange heat with the environment as well as with the furnace.
A heat engine must exchange heat with a low temperature sink as well as a high temperature source to keep operating.
Heat engine that violates the Kelvin-Planck statement of the second law
Clausius statement of the second law
“It is impossible for a self acting machine working in a cyclic process unaided by any external agency, to convey heat from a body at lower temperature to a body at a higher temperature” .
In other word, heat of, itself, cannot flow from a colder to a hotter body.

25. Heat pump that violates the Clausius statement of the second law
Or energy from the surroundings in the form of work or heat has to be expended to force heat to flow from a low-temperature medium to a high-temperature medium.
Thus, the COP of a refrigerator or heat pump must be less than infinity.

26. A violation of either the Kelvin-Planck or Clausius statements of the second law implies a violation of the other. Assume that the heat engine shown below is violating the Kelvin-Planck statement by absorbing heat from a single reservoir and producing an equal amount of work W. The output of the engine drives a heat pump that transfers an amount of heat QL from the low-temperature thermal reservoir and an amount of heat QH + QL to the high-temperature thermal reservoir. The combination of the heat engine and refrigerator in the left figure acts like a heat pump that transfers heat QL from the low-temperature reservoir without any external energy input. This is a violation of the Clausius statement of the second law.

27. The heat lost by the building has to be supplied by the heat pump.
Example 11-4
A heat pump is to be used to heat a building during the winter. The building is to be maintained at 21oC at all times. The building is estimated to be losing heat at a rate of 135,000 kJ/h when the outside temperature drops to -5oC. Determine the minimum power required to drive the heat pump unit for this outside temperature.
21 oC HP
-5 oC
The heat lost by the building has to be supplied by the heat pump.

28. Using the basic definition of the COP

29. 7-39
A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate of heat transfer to the kitchen air. [0.83 kW, 110 kJ/min]
7-40
A commercial heat pump absorbed 10,000 kJ/h from the source, rejects 15,090 kJ/h to the sink, and requires 1.5 kW of power. What is this heat pump’s coefficient of performance?
7-42
A refrigerator used for cooling food in a grocery store is to produce a 10,000 kJ/h cooling effect, and its has a coefficient of performance of How many kilowatts of power will this refrigerator require to operate? [2.06 kW]

30. 7-50
A food refrigerator is to provide a 15,000 kj/h cooling effect while rejecting 22,000 kJ/h of heat. Calculate the COP of this refrigerator. [2.14]
7-52
A heat pump is used to maintain a house at a constant temperature of 23°C. The house is losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/h. For a COP of 2.5, determine the required power input to the heat pump. [6.22 kW]