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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.

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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

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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

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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.

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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.

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Reversible processes

Ideal processes

Irreversible processes

Actual processes

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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:

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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.

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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.

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3 -Mixing of two gases ,

Work should be supplied from the surrounding to separate the two gases.

Hence, irreversible process.

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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 TH to TL .

2. The only way to bring the system back to TL is to cool it by refrigerator.

3. The refrigerator requires work from the surrounding Winput.

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

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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.

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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.

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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.

0T

0Q

0Q

0T

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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 (1769-1832) It is composed of four processes as

follows:

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Process 1-2: A reversible isothermal expansion

The gas is allowed to expand isothermally by receiving heat ( QH) from a hot reservoir.

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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 TH to TL.

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Process 3-4: A reversible isothermal compression

The insulation is removed and the gas is compressed isothermally by rejecting heat (QL) to a cold reservoir.

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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 TL to TH

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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.

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Carnot cycle can be executed in many different ways

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Reversed Carnot Cycle

Process 2-3: The gas expands isothermally at TL while receiving QL from the cold reservoir.Process 3-4: The gas is compressed adiabatically raising its temperature to TH.Process 4-1: The gas is compressed isothermally by rejecting QH to the hot reservoir.

Process 1-2: The gas expands adiabatically (throttling valve) reducing its temp from TH to TL.

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Reversed Carnot Cycle

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Carnot principles1. 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.

Low temperature reservoir at TL

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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.

L

H

revL

H

T

T

Q

Q

cycles reversible ForThe 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 (TH,TL)

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Efficiency of a Carnot Engine For a reversible cycle the amount of heat

transferred is proportional to the temperature of the reservoir.

H

Lrev Q

Q1

H

L

T

T1

Only true for the reversible case

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COP of a Reversible Heat Pump and a Reversible Refrigerator

HLrevHP QQ

COP

1

1,

HL TT1

1

1

1,

LH

revR QQCOP

1

1

LH TT

Only true for the reversible case

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How do Reversible Carnot Heat Engine compare with real engines?

engine heat impossible

engine heat reversible

engine heat leirreversib

rev,th

rev,th

rev,th

th

thermal th

engine heat impossible

engine heat reversible

engine heat leirreversib

rev,th

rev,th

rev,th

th

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orrefrigerat impossible COP

orrefrigerat reversible COP

orrefrigerat leirreversib COP

COP

rev,R

rev,R

rev,R

R

1

1

L

HR

QQ

COP

1

1

L

Hrev,R

TT

,COP

COP of Carnot Refrigerator

How do Carnot Refrigerator compare with real Refrigerator?

COP of Refrigerator

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COP of Carnot Heat PumpCOP of real Heat Pump

H

LHP

QQ

COP

1

1

H

Lrev,HP

TT

COP

1

1

Pump Heat impossible COP

Pump Heat reversible COP

Pump Heat leirreversib COP

COP

rev,HP

rev,HP

rev,HP

HP

How do Carnot Heat Pump compare with real one?

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How to increase the efficiency of a real heat engine?

H

Lrev,th

H

Lth

T

T

Q

Q

1

1

1- Increase TH but you are limited with melting temperature of the engine material.

2- Decrease TL but you are limited with your environment.

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Example (5-8): 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 21oC 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 -5oC. Determine the minimum power required to drive this heat pump.

Sol:

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Example (1)

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Example (2)

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Example (3)

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Example (4)