THE SECOND LAW OF

THERMODYNAMICS

1 By Meng Chamnan GIM

Lesson 5:

Direction of

Spontaneous

Process

By Meng Chamnan 2 GIM

Usefulness of the Second Law

1. Predicting the direction of processes.

2. Establishing conditions for equilibrium.

3. Determining the best theoretical performance of cycles, engines, and other devices.

4. Evaluating quantitatively the factors that preclude the attainment of the best theoretical performance level.

Additional uses of the second law include its roles in

5. Defining a temperature scale independent of the properties of any thermometric substance.

6. Developing means for evaluating properties such as u and h in terms of properties that are more readily obtained experimentally.

By Meng Chamnan 3 GIM

Clausius Statement of the 2nd Law

• It is impossible for any system to operate in such a

way that the sole result would be an energy transfer

by heat from a cooler to a hotter body.

By Meng Chamnan 4 GIM

By Meng Chamnan GIM 5

Example1:

A heat pump receives energy by heat transfer

from the outside air at 0oC and discharges

energy by heat transfer to a dwelling at 20oC.

Is this in violation of the Clausius statement of

the second law of thermodynamics? Explain.

Kelvin–Planck Statement of the 2nd Law

• It is impossible for any system

to operate in a thermodynamic

cycle and deliver a net amount

of energy by work to its

surroundings while receiving

energy by heat transfer from a

single thermal reservoir

By Meng Chamnan 6 GIM

Kelvin-Planck: Single Reservoir

0W

By Meng Chamnan 7 GIM

Kelvin-Planck: Double Reservoir

0W

By Meng Chamnan 8 GIM

By Meng Chamnan GIM 9

Example2:

Air as an ideal gas expands isothermally at 20oC

from a volume of 1 m3 to 2 m3. During this process

there is heat transfer to the air from the

surrounding atmosphere, modeled as a thermal

reservoir, and the air does work. Evaluate the

work and heat transfer for the process, in kJ/kg. Is

this process in violation of the second law of

thermodynamics? Explain.

Reversible and Irreversible

• A process is reversible if both the system

and surroundings can be returned to their

initial states

• A process is called irreversible if the system

and all parts of its surroundings cannot be

exactly restored to their respective initial

states after the process has occurred.

By Meng Chamnan 10 GIM

Irreversibilities

1. Heat transfer through a finite temperature difference

2. Unrestrained expansion of a gas or liquid to a lower pressure

3. Spontaneous chemical reaction

4. Spontaneous mixing of matter at different compositions or states

5. Friction—sliding friction as well as friction in the flow of fluids

6. Electric current flow through a resistance

7. Magnetization or polarization with hysteresis

8. Inelastic deformation

By Meng Chamnan 11 GIM

Internally Reversible Processes

• An internally reversible process is one in

which there are no irreversibilities within the

system.

• Internally reversible process consists of a

series of equilibrium states: It is a

quasiequilibrium process.

By Meng Chamnan 12 GIM

By Meng Chamnan GIM 13

Example3:

Methane gas within a piston–cylinder assembly is

compressed in a quasiequilibrium process. Is this

process internally reversible? Is this process

reversible?

Power Cycles Interacting with Two

Reservoirs

By Meng Chamnan 14 GIM

1 1cycle C

H H

W Q

Q Q

thermal efficiency of the cycle

The Second Law Corollary: Carnot Corollary

• The thermal efficiency of an irreversible power cycle is

always less than the thermal efficiency of a reversible power

cycle when each operates between the same two thermal

reservoirs.

• All reversible power cycles operating between the same two

thermal reservoirs have the same thermal efficiency.

By Meng Chamnan 15 GIM

By Meng Chamnan GIM 16

Example 4:

The data listed below are claimed for a power cycle

operating between reservoirs at 727 and 127oC.

For each case, determine if any principles of

thermodynamics would be violated.

(a) QH = 600 kJ, Wcycle = 200 kJ, QC = 400 kJ.

(b) QH = 400 kJ, Wcycle = 240 kJ, QC = 160 kJ.

(c) QH = 400 kJ, Wcycle = 210 kJ, QC = 180 kJ.

By Meng Chamnan GIM 17

Example 5:

A power cycle operating between two reservoirs

receives energy QH by heat transfer from a hot

reservoir at TH = 2000 K and rejects energy QC by

heat transfer to a cold reservoir at TC = 400 K. For

each of the following cases determine whether the

cycle operates reversibly, irreversibly, or is

impossible:

(a) QH = 1200 kJ, Wcycle = 1020 kJ.

(b) QH = 1200 kJ, QC = 240 kJ.

(c) Wcycle = 1400 kJ, QC = 600 kJ.

(d) η = 40%.

By Meng Chamnan GIM 18

Example 6:

An inventor claims to have developed a power cycle

capable of delivering a net work output of 410 kJ for

an energy input by heat transfer of 1000 kJ. The

system undergoing the cycle receives the heat

transfer from hot gases at a temperature of 500 K and

discharges energy by heat transfer to the atmosphere

at 300 K. Evaluate this claim.

Refrigeration and Heat Pump Cycles

Interacting with Two Reservoirs

By Meng Chamnan 19 GIM

coefficient of performance(COP)

for a refrigeration cycle

coefficient of performance for

a heat pump cycle

C C

cycle H C

Q Q

W Q Q

H H

cycle H C

Q Q

W Q Q

Corollaries for Refrigeration and Heat Pump

Cycles

• The coefficient of performance of an irreversible

refrigeration cycle is always less than the coefficient

of performance of a reversible refrigeration cycle

when each operates between the same two thermal

reservoirs.

• All reversible refrigeration cycles operating between

the same two thermal reservoirs have the same

coefficient of performance

By Meng Chamnan 20 GIM

Kelvin Temperature Scale

By Meng Chamnan 21 GIM

C C

revH Hcycle

Q T

Q T

where “rev cycle” emphasizes that the expression

applies only to systems undergoing reversible cycles

while operating between thermal reservoirs at TC and TH

Performance of Thermodynamic Cycle

By Meng Chamnan 22 GIM

max 1 C

H

T

T Reversible thermal efficiency for

power cycle “Carnot Efficiency”

Reversible COP for refrigeration cycle

maxC

H C

T

T T

Reversible COP for heat pump cycle

maxH

H C

T

T T

By Meng Chamnan GIM 23

Example 7: By steadily circulating a refrigerant at low

temperature through passages in the walls of the freezer

compartment, a refrigerator maintains the freezer

compartment at -5oC when the air surrounding the refrigerator

is at 22oC.

The rate of heat transfer from the

freezer compartment to the refrigerant

is 8000 kJ/h and the power input

required to operate the refrigerator is

3200 kJ/h. Determine the coefficient of

performance of the refrigerator and

compare with the coefficient of

performance of a reversible

refrigeration cycle operating between

reservoirs at the same two

temperatures.

By Meng Chamnan GIM 24

Example 8: The refrigerator shown in

the below picture operates at steady

state with a coefficient of performance

of 4.5 and a power input of 0.8 kW.

Energy is rejected from the refrigerator

to the surroundings at 20oC by heat

transfer from metal coils attached to

the back. Determine

(a) the rate energy is rejected, in kW.

(b) the lowest theoretical temperature

inside the refrigerator, K.

By Meng Chamnan GIM 25

Example 9:

A dwelling requires 6 ×105 Btu per day to maintain its

temperature at 70oF when the outside temperature is 32oF.

(a) If an electric heat pump is used to supply this energy,

determine the minimum theoretical work input for one day of

operation, in Btu/day.

(b) Evaluating electricity at 8 cents per kW·h, determine the

minimum theoretical cost to operate the heat pump, in $/day.

Carnot Cycle

By Meng Chamnan 26 GIM

Carnot cycle introduced in this section provides a specific

example of a reversible power cycle operating between

two thermal reservoirs