2nd Law of Thermodynamics

Lecturer: Professor Stephen T. Thornton

Reading QuizWhich of the following is most true?

A) The second law of thermodynamics is simply a statement of the conservation of energy.

B) The Carnot Engine is the most efficient engine possible.

C) Carnot built his engine as a gift to King Henry VIII.

D) Heat engines normally operate between three thermal reservoirs.

Answer: B

The Carnot cycle and Carnot engine is it!

Last Time

Adiabatic expansion Heat transfer Conduction Convection Radiation

Today

Second Law of Thermodynamics Heat engines Carnot cycle and Carnot engine

If the first law of thermodynamics is about energy conservation, then the 2nd law is about the way in which energy flows.

Examples:A bowl of water sitting in this room does not spontaneously freeze.

It is impossible to construct an engine that can extract thermal energy from a system and turn all that energy into work.

Thermal systems spontaneously change in only certain ways.

2nd Law of ThermodynamicsWe can discuss this law in a number of ways.

The law basically states the way in which heat flow occurs.

Heat flow between two objects brought together in thermal contact always goes from the hotter object to the colder object.

Lots of ways to say the same thing!

Heat Engines

An engine is a device that converts heat into mechanical work.

Engines must operate in cycles in order to be useful. A piston and cylinder must return to original position. The change in internal energy is zero.

An engine operates between two thermal reservoirs.

Schematic Diagram of Heat Engine

, , are positive.

Efficiency

1

h c

h c

h c

h h

c

h

W Q Q

W Q Q

e

Q QWe

Q Q

Qe

Q

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A steam engine is one type of heat engine.

Heat Engines

Do demos

• Heat engine

• Steam engine

cT

Our favorite heat engine.

Reversible processes.

X

hQ

cQ

Remember that thework is equal to thearea under the -curve. Total workhere is work enclosedin cycle.

P V

cT X

hQ

cQ

Carnot Cycle

• Carnot’s cycle represents the most efficient

engine possible.

• It operates between two heat reservoirs.

• All the processes are reversible – two

isothermals and two adiabatics.

• We can show for the Carnot

cycle.

c c

h h

Q T

Q T=

max

max max

1 1

For the highest efficiency, we need themaximum difference of temperatures in thermal reservoirs.

1 for Carnot cycle

Because / ,we have

1

c c

h h

c

h

h h

ch h

h

Q Te

Q T

Te

T

e W Q W eQ

TW e Q Q

T

Conceptual Quiz:A heat engine absorbs 150 J of heat from a hot reservoir and rejects 90 J of it to a cold reservoir. What is the efficiency of this engine? A)       20%B)       40%C)       60%D)       67%E)       90%

1 1c c

h h

Q Te

Q T

Answer: B

901 1 0.40

150c

h

Qe

Q

Conceptual Quiz:For the previous heat engine, you are told the temperature of the hot reservoir is 200 oC and that of the cold reservoir is 11oC. Your response is to

 A)   believe that this is possible.B)   laugh at the idea.C)   contact a patent lawyer immediately.

1 1c c

h h

Q Te

Q T

Answer: A

11 273 2841 1 1 0.4

200 273 473c

h

Te

T

It is not possible to construct an engine whose sole effect is to transform a given amount of heat completely into work!

Another statement of 2nd Law of Thermodynamics

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Thermography—the detailed measurement of radiation from the body—can be used in medical imaging. Warmer areas may be a sign of tumors or infection; cooler areas on the skin may be a sign of poor circulation.

Conceptual QuizConceptual Quiz

Given your experience of

what feels colder when you

walk on it, which of the

surfaces would have the

highest thermal

conductivity?

A) a rug

B) a steel surface

C) a concrete floor

D) has nothing to do withthermal conductivity

Conceptual QuizConceptual Quiz

Given your experience of

what feels colder when you

walk on it, which of the

surfaces would have the

highest thermal

conductivity?

A) a rug

B) a steel surface

C) a concrete floor

E) has nothing to do withthermal conductivity

The heat flow rate is k A (T1 − T2)/L. All things being

equal, bigger k leads to bigger heat loss.

From the book: Steel = 40, Concrete = 0.84,

Human tissue = 0.2, Wool = 0.04, in units of J/(s.m.C°).

Heat engine and refrigerator

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This figure shows more details of a typical refrigerator.

We analyze refrigerators differently. We want to remove as much heat Qc as possible for the least amount of work.

Coefficient of Performance or COP

COP =

Remember that This is the amount of heat exhausted into kitchen.For an air conditioner, this is the heat exhausted to the outside.

c

h c

Q

W

Q Q W

Air conditioner and heat pump

Maximize Qc

Maximize Qh

inside house

Heat house

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A heat pump can heat a house in the winter:

For an ideal, reversible heat pump (i.e. Carnot cycle), we have

1

1

ch c h

h

ch

h

QW Q Q Q

Q

TW Q

T

c c

hh

Q TTQ

To minimize W we want temperatures to be similar.

Conceptual Quiz:A heat engine exhausts heat QC to a cold reservoir. The amount of work done by the engine (give best answer) A)       must be QC .B)       must be greater than QC .C)       must be less than QC .D)       could be greater than QC . 

h cW Q Q

Answer: D

W = Qh – Qc > 0

We know that Qh > Qc, but that is about all we know.

The work could be Qc, but we can’t tell.

The work can be greater or less than Qc, but we can’t know.

The only reasonable answer is D.

Conceptual QuizConceptual Quiz

The heat engine below is: A) a reversible (Carnot) heat engine

B) an irreversible heat engine

C) a hoax

D) none of the above

1 1

For what??

c c

h h

Q Te

Q T

310 KCT =

Conceptual QuizConceptual Quiz

The heat engine below is: A) a reversible (Carnot) heat engine

B) an irreversible heat engine

C) a hoax

D) none of the above

Carnot e = 1 − TC/TH = 1 − 270/600 = 0.55.

But by definition e = 1 − QL/QH

= 1 − 4000/8000 = 0.5, smaller

than Carnot e, thus irreversible.

310 KCT =

Hiker as Heat Engine. Assume that a 65 kg hiker needs 4.3 x 103 kcal of energy to supply a day’s worth of metabolism. Estimate the maximum height the person can climb in one day, using only this amount of energy. As a rough prediction, treat the person as an isolated heat engine, operating between the internal temperature of 37°C (98.6°F) and the ambient air temperature of 20°C.

Heat Pump. A heat pump is used to keep a house warm at 22°C. How much work is required of the pump to deliver 3100 J of heat into the house if the outdoor temperature is (a) 0°C, (b) -15°C. Assume ideal (Carnot) behavior.