jj207 thermodynamic topic 4 second law of thermodynamics

JJ207-THERMODYNAMICS 1 Topic 4- Second Law of Thermodynamics

TOPIC 4 SECOND LAW OF THERMODYNAMICS

At the end of the topic you will be able to:

Relate the concept of the second law of Thermodynamics. Explain the concept of the second law of thermodynamics. Define and explain the principles of a heat engine and a reverse heat engine. Analyze the essentials of heat engine according to working substance, heat

source, mechanical arrangement and working cycle. Review the energy balance for a heat engine (as a black box) and efficiency. Apply the concept of the second law of Thermodynamics. Explain the maximum possible efficiency (Carnot efficiency). Explain the reversible and irreversible processes. Evaluate the second law limitation. Describe the Carnot cycle, Carnot principles, Carnot heat engines, Carnot

refrigerator heat pump, Carnot heat engine, Carnot heat refrigerator and heat pump. Explain the entropy principles and isentropic processes. Describe the property diagrams involving entropy and the T-s relation. Explain the entropy change for liquids and solids and ideal gases. Explain the isentropic efficiencies of steady-flow devices. Analyze the entropy balance. Describe cyclic and non-cyclic processes and their application on the open and

closed systems. Apply the second law of thermodynamics in complete cycles, steady flow

system and closed volume.

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4.0 INTRODUCTION

According to the First Law of Thermodynamics as stated in Topic 2, when a system undergoes a complete cycle, then the net heat supplied is equal to the net work done.

dQ = dWThis is based on the conservation of energy principle, which follows from the observation on natural events.

The Second Law of Thermodynamics, which is also a natural law, indicates that;

In symbols,Q1 – Q2 = W (4.1)

To enable the second law to be considered more fully, the heat engine must be discussed.

4.1 The heat engine and reverse heat engine (heat pump)

Some DefinitionsTo express the second law in a workable form, we need the following definitions:

Heat (Thermal) ReservoirA 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.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.

Work ReservoirA work reservoir is a sufficiently large system in stable equilibrium to which and from which finite amounts of work can be transferred adiabatically without any change in its pressure.

Thermodynamic CycleA system has completed a thermodynamic cycle when the system undergoes a series of processes and then returns to its original state, so that the properties of the system at the end of the cycle are the same as at its beginning.

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Although the net heat supplied in a cycle is equal to the net work done, the gross heat supplied must be greater than the work done; some heat must always be rejected by the system.

…The Second Law of Thermodynamics


Reversible ProcessesA reversible process is a quasiequilibrium, or quasistatic, process with a more restrictive requirement. In reversible process, both the system and surrounding can be returned to their initial states.

Internally Reversible ProcessThe internally reversible process is a quasiequilibrium process, which once having taken place, can be reversed and in so doing leave no change in the system. This says nothing about what happens to the surroundings about the system.

Totally or Externally Reversible ProcessThe externally reversible process is a quasiequilibrium process, which once having taken place, can be reversed and in so doing leave no change in the system or surroundings.

Irreversible ProcessAn irreversible process is a process that is not reversible. In irreversible process, the system and all parts of its surrounding cannot be exactly restored to their respective initial state after the process has occurred.

All real processes are irreversible. Irreversible processes occur because of the following:

FrictionUnrestrained expansion of gasesHeat transfer through a finite temperature differenceMixing of two different substancesHysteresis effectsI2R losses in electrical circuitsAny deviation from a quasistatic process

4.1.1 Heat engine

We know from experience that work can be converted to heat directly and completely, but converting heat to work requires the use of some special devices. These devices are called heat engines.

A heat engine is a system operating in a complete cycle and developing net work from a supply of heat. The second law implies that a source of heat supply (or hot reservoir) and a sink (or cold reservoir) for the rejection of heat are both necessary, since some heat must always be rejected by the system.

Heat engines differ considerably from one another, but all can be characterised by the following: They receive heat from a high-temperature source (for example solar energy, oil

furnace, nuclear reactor, steam boiler, etc.)

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They convert part of this heat to work (usually in the form of a rotating shaft, for example gas turbine, steam turbine, etc.)

They reject the remaining waste heat to a low-temperature sink (for example the atmosphere, rivers, condenser, etc.)

They operate on a cycle.

A diagrammatic representation of a heat engine is shown in Fig. 4.1

Heat engines and other cyclic devices usually involve a fluid that moves to and fro from which heat is transferred while undergoing a cycle. This fluid is called the working fluid.

The work-producing device that best fits into the definition of a heat engine are: The steam power plant The close cycle gas turbine

By the first law, in a complete cycle,Net heat supplied = Net work done

Referring to Fig. 4.1, from equation dQ = dW, we have, QH – QL = W

By the second law, the gross heat supplied must be greater than the net work done,

i.e. QH > W

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High-temperatureReservoir, at TH

Low-temperatureReservoir, TL

HEAT

ENGINE

QH

QL

WORK OUTPUTW = QH – QL

Note:QH = The heat supplied from the

source.

W = The net work done.

QL = The heat rejected.

Figure 4.1 Part of the heat received by the heat engine is converted to work,while the rest is rejected to cold reservoir.

Heat is transferred to a heat engine from a furnace at a rate of 80 MW. If the rate of waste heat rejection to a nearby river is 45 MW, determine the net work done and the thermal efficiency for this heat engine.


The thermal efficiency of a heat engine is defined as the ratio of the net work done in the cycle to the gross heat supplied in the cycle. It is usually expressed as a percentage.

Referring to Fig. 4.1,

Thermal efficiency, th (4.2)

Substituting equation 4.1,

th

th in terms of heat (4.3)

th in terms of temperature (4.4)

It can be seen that the second law implies that the thermal efficiency of a heat engine

must always be less than 100% (QH > W ).

Example 4.1

Solution to Example 4.1

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FURNACE

RIVER

HEAT

ENGINE

QH = 80 MW

QL = 45 MW

W = ?


A schematic of the heat engine is given in the diagram above. The furnace serves as the high-temperature reservoir for this heat engine and the river as the low-temperature reservoir.

Assumption: Heat lost through the pipes and other components are negligible.

Analysis: The given quantities can be expressed in rate form as;QH = 80 MWQL = 45 MW

From equation 4.1, the net work done for this heat engine is;W = QH – QL

= (80 – 45) MW= 35 MW

Then from equation 4.2, the thermal efficiency is easily determined to be

th

That is, the heat engine converts 43.75 percent of the heat it receives to work.

4.1.2 Reversed heat engine (heat pump)

The first and second laws apply equally well to cycles working in the reverse direction to those of heat engine. In general, heat only flows from a high-temperature source to a low-temperature sink. However, a reversed heat engine can be utilized to pump the heat from a low-temperature region to a high-temperature region. The reversed heat engine is called heat pump.

A heat pump is a thermodynamic system operating in a thermodynamic cycle which 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 low-temperature media. The heat pump also operates on a thermodynamic cycle but rejects heat to the high-temperature media.

The following figure illustrates a refrigerator as a heat pump operating in a thermodynamic cycle.

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Fig. 4.2 Basic component of a refrigeration system and typical operating conditions

In the case of a reversed cycle, the net work done on the system is equal to the net heat rejected by the system. Such cycles occur in heat pumps and refrigerators. The equivalent diagram of the heat pump (or refrigerator) is shown in Fig. 4.3.

In the heat pump (or refrigerator) cycle, an amount of heat, QL, is supplied from the cold reservoir, and an amount of heat, QH, is rejected to the hot reservoir.

QH = W + QL (4.4)

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High-temperatureReservoir, TH

Low-temperatureReservoir, TL

HEAT

PUMP

QH

QL

WORK INPUTW

QH = W + QL

Figure 4.3 Reverse heat engine (heat pump)


In the second law, we can say that work input is essential for heat to be transferred from the cold to the hot reservoir,i.e. W > 0

The first law sets no limit on the percentage of heat supplied, which can be converted into work. Nor does it indicate whether the energy conversion process is physically possible or impossible. We shall see, though, that a limit is imposed by the Second Law of Thermodynamics, and that the possibility or otherwise of a process can be determined through a property of the working fluid called entropy.

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.

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.

For the refrigerator the desired result is the heat supplied at the low temperature and the input is the net work into the device to make the cycle operate.

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4.2 The Carnot Cycle

French military engineer Nicolas Sadi Carnot (1769-1832) was among the first to study the principles of the second law of thermodynamics. Carnot was the first to introduce the concept of cyclic operation and devised a reversible cycle that is composed of four reversible processes, two isothermal and two adiabatic.

The Carnot CycleProcess 1-2 Reversible isothermal heat addition at high temperature, TH > TL to the

working fluid in a piston--cylinder device which does some boundary work.Process 2-3 Reversible adiabatic expansion during which the system does work as the

working fluid temperature decreases from TH to TL.Process 3-4 The system is brought in contact with a heat reservoir at TL < TH and a

reversible isothermal heat exchange takes place while work of compression is done on the system.

Process 4-1 A reversible adiabatic compression process increases the working fluid temperature from TL to TH.

You may have observed that the power cycle operates in the clockwise direction when plotted on a process diagram. The Carnot cycle may be reversed, in which it operates as a refrigerator. The refrigeration cycle operates in the counter clockwise direction.

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4.2.1 Carnot Principles

The second law of thermodynamics puts limits on the operation of cyclic devices as expressed by the Kelvin-Planck and Clausius statements. A heat engine cannot operate by exchanging heat with a single heat reservoir, and a refrigerator cannot operate without net work input from an external source.

Considering heat engines operating between two fixed temperature reservoirs at TH > TL. We draw two conclusions about the thermal efficiency of reversible and irreversible heat engines, known as Carnot Principles.

(a) The efficiency of an irreversible heat engine is always less than the efficiency of a reversible one operating between the same two reservoirs.

ηth < ηth, Carnot

(b) The efficiencies of all reversible heat engines operating between same two constant temperature heat reservoirs have the same efficiency.

As the result of the above, Lord Kelvin in 1848 used energy as a thermodynamic property to define temperature and devised a temperature scale that is independent of the thermodynamic substance. He considered the following arrangement:

Since the thermal efficiency in general is

th

The Carnot thermal efficiency becomes

th

This is the maximum possible efficiency of a heat engine operating between two heat reservoirs at temperatures TH and TL. Note that the temperatures are absolute temperatures.

These statements form the basis for establishing an absolute temperature scale, also called the Kelvin scale, related to the heat transfers between a reversible device and the high- and low-temperature heat reservoirs by

Then the QH/QL ratio can be replaced by TH/TL for reversible devices, where TH and TL are the absolute temperatures of the high- and low-temperature heat reservoirs, respectively. This result is only valid for heat exchange across a heat engine operating between two constant temperature heat reservoirs. These results do not apply when the heat exchange is occurring with heat sources and sinks that do not have constant temperature.

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The thermal efficiencies of actual and reversible heat engines operating between the same temperature limits compare as follows:

Example 5-2A Carnot heat engine receives 500 kJ of heat per cycle from a high-temperature heat reservoir at 652oC and rejects heat to a low-temperature heat reservoir at 30oC.Determine(a) The thermal efficiency of this Carnot engine.(b) The amount of heat rejected to the low-temperature heat reservoir.

a)

b)

Example 5-3

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An inventor claims to have invented a heat engine that develops a thermal efficiency of 80% when operating between two heat reservoirs at 1000 K and 300 K. Evaluate his claim.

Answer)

The claim is false since no heat engine may be more efficient than a Carnot engine operating between the heat reservoirs.

Example 5-4An inventor claims to have developed a refrigerator that maintains the refrigerated space at 2oC while operating in a room where the temperature is 25 oC and has a COP of 13.5. Is there any truth to his claim?

Answer)

The claim is false since no refrigerator may have a COP larger than the COP for the reversed Carnot device.

4.3 Entropy

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The first law applied to a heat engine or energy conversion process is merely an energy balance. However, the first law does not indicate the possibility or impossibility of the process, and we know from our everyday experience that some energy conversions are never observed. In previous topic, internal energy which is an important property, arised as a result of the First Law of Thermodynamics. Another important property, entropy, follows from the second law.

Considering 1 kg of fluid, the units of entropy are given by kJ/kg divided by K. The the unit of specific entropy, s, is kJ/kg K. The symbol S will be used for the entropy of mass, m, of a fluid,i.e. S = ms kJ/K

The change of entropy is more important than its absolute value, and the zero of entropy can be chosen quite arbitrarily. For example, in the Steam Tables the specific entropy at saturated liquid is put equal to zero at 0.01oC; in tables of refrigerants the specific entropy at saturated liquid is put equal to zero at – 40oC.

For all working substances, the change of entropy is given by

dsdQ

T (4.5)

Re-writing equation 9.5 we havedQ = T ds

or for any reversible process

(4.6)

The equation 4.7 below is analogous to equation 4.6 for any reversible process

(4.7)

Thus, as there is a diagram on areas that represent work done in a reversible process, there is also a diagram on areas that represent heat flow in a reversible process. These diagrams are the P-v and the T-s diagrams respectively, as shown in Figs. 4.2-1 and 4.2-2.

For a reversible process from point 1 to point 2:

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in Fig. 4.2-1, the shaded area , represents work done; and

in Fig. 4.2.2, the shaded area , represents heat flow.

Therefore, one great use of property entropy is that it enables a diagram to be drawn showing the area that represents heat flow in a reversible process.

Isentropic ProcessThe reversible, adiabatic process is called an isentropic process. Entropy change is caused by heat transfer and irreversibilities. Heat transfer to a system increases the entropy, heat transfer from a system decreases it. The effect of irreversibilities is always to increase the entropy. In fact, a process in which the heat transfer is out of the system may be so irreversible that the actual entropy change is positive. Friction is one source of irreversibilities in a system.

The adiabatic, reversible process is a constant entropy process and is called isentropic. As will be shown later for an ideal gas, the adiabatic, reversible process is the same as the polytropic process where the polytropic exponent n = γ = Cp/Cv.

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1

2

P

vdv

P

1

2

T

sds

T

Figure 4.2.1 Work done Figure 4.2.2 Heat flow

jj207 thermodynamic topic 4 second law of thermodynamics

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