SECOND LAW OF THERMODYNAMICS

2ND Law of Thermodynamics

• Puts a limitation on the conversion of some forms of energy

• Determines the scope of an energy conversion and if an energy conversion is possible

• Provides means of evaluating the thermodynamic performance of systems and processes so that sound design decisions can be made

KELVIN-PLANCK STATEMENT

Kelvin-Planck Statement of the 2nd Law“It is impossible to construct a heat engine that operates in

a cycle, receives a high-temperature body, and does an equal amount of work. This implies that it is impossible to build a heat engine that has a thermal efficiency of 100%. The thermal efficiency of practical heat engines typically ranges from 10 to 40%. Thus in practice, some portion of the heat supplied from a high-temperature source is always rejected to a low-temperature sink.”

TWO PRINCIPLES DRAWN FROM KELVIN-PLANCK

STATEMENT

Two Principles drawn from Kelvin-Planck Statement

1. Cycle efficiency of an irreversible power cycle is always less than the cycle efficiency of a reversible power cycle when each operates between the same reservoirs

2. All reversible power cycles operating between the same two thermal reservoirs have the same cycle efficiency. It implies that the specific states, working fluid, or specific processes of the reversible power cycle do not affect the cycle efficiency.

Reversible Process

➢Process that can be reversed and leaves no change in either system or surroundings.

Internally reversible process

➢Process in which the system can be returned to its initial equilibrium state without leaving any permanent changes in the system

Totally reversible process

➢Process in which both system and its surroundings must be capable of being returned to their initial equilibrium states without leaving any permanent changes in both the system and surroundings

Irreversibility

➢Representing a loss of work

A process is called irreversible if the system and all the parts of its surrounding cannot be exactly restored to their respective initial states after the process has occurred.

Common Causes of Irreversibility1. Electric Resistance

2. Inelastic Deformation

3. Viscous flow of a fluid

4. Solid-solid friction

5. Heat transfer from a finite temperature difference

6. Fluid flow through valves and porous plugs

7. Mixing of Dissimilar gases or liquids

8. Mixing of identical fluids initially at different pressures and temperatures

Thermal efficiency

➢Ratio of output (the energy sought) to the input (the energy supplied)

Thermal Reservoir

➢Body to which and from which heat can be transferred indefinitely without a change in its temperature

➢e.g. atmosphere, oceans, and lakes

CARNOT CYCLE

Carnot Cycle

• The most efficient cycle that can operate between two constant-temperature reservoirs

• A totally reversible cycle

• Named after the French engineer, Nicolas Leonard SadiCarnot

Four Reversible Processes of Carnot Cycle1. Reversible Isothermal Expansion (heat transfers to fluid)

2. Reversible Adiabatic Expansion (temperature decreases)

3. Reversible Isothermal Compression (heat transfer to reservoir)

4. Reversible Adiabatic Compression (temperature increases)

Efficiency of a Carnot Cycle

• 1st Proposition

• 2nd Proposition

Carnot Heat Engine

• A device that operates in a cycle and produces a net positive work while exchanging heat across boundaries

Carnot Heat Engine

• Thermal efficiency:

*

net H Lth

input H

th th th

W T T

Q T

Carnot Ideal Actual

Example

• A heat engine operates on the Carnot cycle. It produces 50 kW of power while operating between limits of 800˚C and 100˚C. Determine the engine efficiency and the amount of heat added.

CLAUSIUS STATEMENT OF THE SECOND LAW

Clausius Statement of the Second Law• States that it is impossible to construct a refrigerator that

operates without an input of work.

• Simply means that heat cannot flow by itself from a low temperature to a high temperature

REVERSE CARNOT CYCLE

Carnot Refrigerator

• Coefficient of Performance (COP)

*Reverse Carnot COP>Ideal COP>Actual COP

L L

net H L

Q TCOP

W T T

Example

A refrigerator maintains the cooled space at 2˚C when the ambient air around the refrigerator is 25˚C. The refrigerator has a coefficient of performance of 2.5. The rate of cooling in the refrigerated space is 8000 kJ/hr.

a) Determine the power consumption and the heat-transfer rate

b) Suppose the refrigerator with a Carnot refrigerator, determine its COP

Carnot heat pump

• Used to maintain the temperature of a heated space at a higher temperature than that of the environment.

• The measure of its performance is called the Performance Factor.

Reverse Carnot Ideal Actual *PF >PF >PF

H H

net H L

Q TPF

W T T

Example

An air-source heat pump is used to provide heat in a house during the winter season. The house is to be maintained at 21˚C, and on a typical day the heat loss from the house amounts to 75000 kJ/hr when outdoor air temperature is -4˚C. The heat pump has a performance factor of 3.7 under these conditions.

a) Determine the power consumption of the heat pump.

b) Suppose the heat pump is replaced with a Carnot heat pump, determine it PF.

Entropy

• The change in entropy of the universe is the measure of irreversibility for a process

Note:

1. Total change of entropy is zero for all reversible processes

2. Total change of entropy will be positive for all irreversible processes.

3. Total change of entropy will never be negative.

Thermodynamic Design Principle

• An optimum design is one that accomplishes the given objectives and results in a minimum increase in the entropy of the universe.

Uses of the Second Law of Thermodynamics

• Determine the maximum possible efficiencies of heat engines;

• Determine the maximum coefficients of performance of refrigerators;

• Determine whether any particular process we are considering is possible or impossible;

Uses of the Second Law of Thermodynamics

• Determine the best theoretical performance of cycles, engines, and other devices; and

• Evaluate quantitatively the factors that prevent the attainment of the best theoretical performance level.

Activity

• An inventor claims to have developed a refrigeration unit that maintains the refrigerated space at -10˚C while operating in a room where the temperature is 25˚C, and that has a coefficient of performance of 8.5. How would you evaluate his claim? If he is claiming a coefficient of performance of 7.0, how would you validate his claim?