Physics 207: Lecture 27, Pg 1 Lecture 27 Goals: Ch. 18 Ch. 18 Qualitatively understand 2 nd Law of...

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Physics 207: Lecture 27, Pg 1 Lecture 27 Goals: Goals: Ch. 18 Ch. 18 Qualitatively understand 2 Qualitatively understand 2 nd nd Law of Law of Thermodynamics Thermodynamics Ch. 19 Ch. 19 Understand the relationship between work and heat in a cycling process Follow the physics of basic heat engines and refrigerators. Recognize some practical applications in real devices. Know the limits of efficiency in a heat engine. Assignment Assignment HW11, Due Tues., May 5 th HW12, Due Friday, May 9 th For Thursday, Read through all of Chapter 20

Transcript of Physics 207: Lecture 27, Pg 1 Lecture 27 Goals: Ch. 18 Ch. 18 Qualitatively understand 2 nd Law of...

Page 1: Physics 207: Lecture 27, Pg 1 Lecture 27 Goals: Ch. 18 Ch. 18 Qualitatively understand 2 nd Law of Thermodynamics Qualitatively understand 2 nd Law of.

Physics 207: Lecture 27, Pg 1

Lecture 27 Goals:Goals:

• Ch. 18Ch. 18

• Qualitatively understand 2Qualitatively understand 2ndnd Law of Thermodynamics Law of Thermodynamics

• Ch. 19Ch. 19 Understand the relationship between work and heat in a cycling process Follow the physics of basic heat engines and refrigerators. Recognize some practical applications in real devices. Know the limits of efficiency in a heat engine.

• AssignmentAssignment HW11, Due Tues., May 5th HW12, Due Friday, May 9th For Thursday, Read through all of Chapter 20

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Physics 207: Lecture 27, Pg 2

The need for something else: Entropy

You have an ideal gas in a box of volume V1. Suddenly you remove the partition and the gas now occupies a larger volume V2.

(1) How much work was done by the system?

(2) What is the final temperature (T2)?

(3) Can the partition be reinstalled with all of the gas molecules back in V1?

P

V1

P

V2

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Physics 207: Lecture 27, Pg 3

Free Expansion and Entropy

You have an ideal gas in a box of volume V1. Suddenly you remove the partition and the gas now occupies a larger volume V2.

(3) Can the partition be reinstalled with all of the gas molecules back in V1

(4) What is the minimum process necessary to put it back?

P

V1

P

V2

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Physics 207: Lecture 27, Pg 4

Free Expansion and Entropy

You have an ideal gas in a box of volume V1. Suddenly you remove the partition and the gas now occupies a larger volume V2.

(4) What is the minimum energy process necessary to put it back?

Example processes:

A. Adiabatic Compression followed by Thermal Energy Transfer

B. Cooling to 0 K, Compression, Heating back to original T

P

V1

P

V2

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Physics 207: Lecture 27, Pg 6

Modeling entropy

I have a two boxes. One with fifty pennies. The other has none. I flip each penny and, if the coin toss yields heads it stays put. If the toss is “tails” the penny moves to the next box.

On average how many pennies will move to the empty box?

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Physics 207: Lecture 27, Pg 7

Modeling entropy

I have a two boxes, with 25 pennies in each. I flip each penny and, if the coin toss yields heads it stays put. If the toss is “tails” the penny moves to the next box. On average how many pennies will move to the other box? What are the chances that all of the pennies will wind up in

one box?

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Physics 207: Lecture 27, Pg 8

2nd Law of Thermodynamics

Second law: “The entropy of an isolated system never decreases. It can only increase, or, in equilibrium, remain constant.”

The 2nd Law tells us how collisions move a system toward equilibrium.

Order turns into disorder and randomness.

With time thermal energy will always transfer from the hotter to the colder system, never from colder to hotter.

The laws of probability dictate that a system will evolve towards the most probable and most random macroscopic state

Entropy measures the probability that a macroscopic state will occur or, equivalently, it measures the amount of disorder in a system

IncreasingEntropy

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Physics 207: Lecture 27, Pg 11

Reversible vs Irreversible

The following conditions should be met to make a process perfectly reversible:1. Any mechanical interactions taking place in the process should be frictionless.2. Any thermal interactions taking place in the process should occur across infinitesimal temperature or pressure gradients (i.e. the system should always be close to equilibrium.)

Based on the above answers, which of the following processes are not reversible?1. Melting of ice in an insulated (adiabatic) ice-water mixture at

0°C.2. Lowering a frictionless piston in a cylinder by placing a bag of

sand on top of the piston.3. Lifting the piston described in the previous statement by

removing one grain of sand at a time.4. Freezing water originally at 5°C.

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Physics 207: Lecture 27, Pg 12

Reversible vs Irreversible

The following conditions should be met to make a process perfectly reversible:1. Any mechanical interactions taking place in the process should be frictionless.2. Any thermal interactions taking place in the process should occur across infinitesimal temperature or pressure gradients (i.e. the system should always be close to equilibrium.)

Based on the above answers, which of the following processes are not reversible?1. Melting of ice in an insulated (adiabatic) ice-water mixture at

0°C.2. Lowering a frictionless piston in a cylinder by placing a bag of

sand on top of the piston.3. Lifting the piston described in the previous statement by

removing one grain of sand at a time.4. Freezing water originally at 5°C.

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Physics 207: Lecture 27, Pg 16

Heat Engines and Refrigerators Heat Engine: Device that transforms heat into work ( Q W) It requires two energy reservoirs at different temperatures

An thermal energy reservoir is a part of the environment so large with respect to the system that its temperature doesn’t change as the system exchanges heat with the reservoir.

All heat engines and refrigerators operate between two energy reservoirs at different temperatures TH and TC.

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Physics 207: Lecture 27, Pg 17

For practical reasons, we would like an engine to do the maximum amount of work with the minimum amount of fuel. We can measure the performance of a heat engine in terms of its thermal efficiency η (lowercase Greek eta), defined as

We can also write the thermal efficiency as

Heat Engines

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Physics 207: Lecture 27, Pg 18

Consider two heat engines: Engine I:

Requires Qin = 100 J of heat added to system to get W=10 J of work (done on world in cycle)

Engine II: To get W=10 J of work, Qout = 100 J of heat is

exhausted to the environment

Compare I, the efficiency of engine I, to II, the efficiency of engine II.

Exercise Efficiency

h

c

h

ch

h Q

Q

Q

QQ

Q

W

1cycle

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Physics 207: Lecture 27, Pg 19

Compare I, the efficiency of engine I, to II, the efficiency of engine II. Engine I:

Requires Qin = 100 J of heat added to system to get W=10 J of work (done on world in cycle)

= 10 / 100 = 0.10 Engine II:

To get W=10 J of work, Qout = 100 J of heat is exhausted to the environment

Qin = W+ Qout = 100 J + 10 J = 110 J = 10 / 110 = 0.09

Exercise Efficiency

h

c

h

ch

h Q

Q

Q

QQ

Q

W

1cycle

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Physics 207: Lecture 27, Pg 20

Refrigerator (Heat pump)

Device that uses work to transfer heat from a colder object to a hotter object.

payyou What getyou What

In

Cold WQK

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Physics 207: Lecture 27, Pg 21

The best thermal engine ever, the Carnot engine A perfectly reversible engine (a Carnot engine) can be

operated either as a heat engine or a refrigerator between the same two energy reservoirs, by reversing the cycle and with no other changes.

A Carnot cycle for a gas engine consists of two isothermal processes and two adiabatic processes

A Carnot engine has max. thermal efficiency, compared with any other engine operating between TH and TC

A Carnot refrigerator has a maximum coefficient of performance, compared with any other refrigerator operating between TH and TC.

Hot

Cold1Carnot TT

ColdHot

Cold

Carnot TTTK

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Physics 207: Lecture 27, Pg 22

The Carnot Engine

All real engines are less efficient than the Carnot engine because they operate irreversibly due to the path and friction as they complete a cycle in a brief time period.

Carnot showed that the thermal efficiency of a Carnot Carnot showed that the thermal efficiency of a Carnot engine is:engine is:

hot

coldcycleCarnot T

T1

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Physics 207: Lecture 27, Pg 23

Problem

You can vary the efficiency of a Carnot engine by varying the temperature of the cold reservoir while maintaining the hot reservoir at constant temperature.

Which curve that best represents the efficiency of such an engine as a function of the temperature of the cold reservoir?

Temp of cold reservoir

hot

coldcycleCarnot T

T1

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Physics 207: Lecture 27, Pg 26

Other cyclic processes: Turbines A turbine is a mechanical device that extracts thermal energy from

pressurized steam or gas, and converts it into useful mechanical work. 90% of the world electricity is produced by steam turbines.

Steam turbines &jet engines use a Brayton cycle

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Physics 207: Lecture 27, Pg 27

Steam Turbine in Madison

MG&E, the electric power plan in Madison, boils water to produce high pressure steam at 400°C. The steam spins the turbine as it expands, and the turbine spins the generator. The steam is then condensed back to water in a Monona-lake-water-cooled heat exchanger, down to 20°C.

Carnot Efficiency?

56.011 673293

Carnot Hot

Cold KK

TT

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Physics 207: Lecture 27, Pg 28

The Sterling Cycle

Return of a 1800’s thermodynamic cycle

Isothermal expansion

Isothermal compression

SRS Solar System (~27% eff.)

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Physics 207: Lecture 27, Pg 29

Sterling cycles

Gas

T=TH

Gas

T=TH

Gas

T=TC

Gas

T=TC

1

1 2

34

V

P

TC

TH

Va Vb

1 2

34

x

start

1 Q, V constant 2 Isothermal expansion ( Won system < 0 )

3 Q, V constant 4 Q out, Isothermal compression ( Won sys> 0) 1 Q1 = nR CV (TH - TC)

2 Won2 = -nR TH ln (Vb / Va)= -Q2

3 Q3 = nR CV (TC - TH)

4 Won4 = -nR TL ln (Va / Vb)= -Q4

QCold = - (Q3 + Q4 )

QHot = (Q1 + Q2 )

= 1 – QCold / QHot

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Physics 207: Lecture 27, Pg 30

Carnot = 1 - Qc/Qh = 1 - Tc/Th Carnot Cycle Efficiency

Power from ocean thermal gradients… oceans contain large amounts of energy

See: http://www.nrel.gov/otec/what.html

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Physics 207: Lecture 27, Pg 31

Ocean Conversion Efficiency

Carnot = 1 - Tc/Th = 1 – 275 K/300 K

= 0.083 (even before internal losses and assuming a REAL cycle)

Still: “This potential is estimated to be about 1013 watts of base load power generation, according to some experts. The cold, deep seawater used in the OTEC process is also rich in nutrients, and it can be used to culture both marine organisms and plant life near the shore or on land.”

“Energy conversion efficiencies as high as 97% were achieved.”

See: http://www.nrel.gov/otec/what.html

So =1-Qc/Qh is always correct but

Carnot =1-Tc/Th only reflects a Carnot cycle

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Physics 207: Lecture 27, Pg 32

Internal combustion engine: gasoline engine

(Adiabats)

A gasoline engine utilizes the Otto cycle, in which fuel and air are mixed before entering the combustion chamber and are then ignited by a spark plug.

Otto Cycle

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Physics 207: Lecture 27, Pg 33

Internal combustion engine: Diesel engine

A Diesel engine uses compression ignition, a process by which fuel is injected after the air is compressed in the combustion chamber causing the fuel to self-ignite.

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Physics 207: Lecture 27, Pg 34

Thermal cycle alternatives Fuel Cell Efficiency (from wikipedia)

Fuel cells do not operate on a thermal cycle. As such, they are not constrained, as combustion engines are, in the same way by thermodynamic limits, such as Carnot cycle efficiency. The laws of thermodynamics also hold for chemical processes (Gibbs free energy) like fuel cells, but the maximum theoretical efficiency is higher (83% efficient at 298K ) than the Otto cycle thermal efficiency (60% for compression ratio of 10 and specific heat ratio of 1.4).

Comparing limits imposed by thermodynamics is not a good predictor of practically achievable efficiencies

The tank-to-wheel efficiency of a fuel cell vehicle is about 45% at low loads and shows average values of about 36%. The comparable value for a Diesel vehicle is 22%.

Honda Clarity (now leased in CA and gets~70 mpg equivalent)

This does not include H2

production & distribution

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Physics 207: Lecture 27, Pg 35

Fuel Cell Structure

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Physics 207: Lecture 27, Pg 36

Problem-Solving Strategy: Heat-Engine Problems

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Physics 207: Lecture 27, Pg 37

Going full cycle 1 mole of an ideal gas and PV= nRT T = PV/nR

T1 = 8300 0.100 / 8.3 = 100 K T2 = 24900 0.100 / 8.3 = 300 K

T3 = 24900 0.200 / 8.3 = 600 K T4 = 8300 0.200 / 8.3 = 200 K

(Wnet = 16600*0.100 = 1660 J)12

Eth= 1.5 nR T = 1.5x8.3x200 = 2490 J

Wby=0 Qin=2490 J QH=2490 J 23

Eth= 1.5 nR T = 1.5x8.3x300 = 3740 J

Wby=2490 J Qin=3740 J QH= 6230 J 34

Eth = 1.5 nR T = -1.5x8.3x400 = -4980 J

Wby=0 Qin=-4980 J QC=4980 J 41

Eth = 1.5 nR T = -1.5x8.3x100 = -1250 J

Wby=-830 J Qin=-1240 J QC= 2070 J

QH(total)= 8720 J QC(total)= 7060 J =1660 / 8720 =0.19 (very low)

V

P

100liters

200liters

1

2 3

4

24900N/m2

8300N/m2

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Physics 207: Lecture 27, Pg 39

Lecture 27

• AssignmentAssignment HW11, Due Tues., May 5th HW12, Due Friday, May 9th For Thursday, Read through all of Chapter 20