Chapter 16 Lecture

Chapter 16: The Second Law of Thermodynamics

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The second law of thermodynamics

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Goals

• To examine the directions of thermodynamic processes.

• To study heat engines.• To overview internal combustion engines and

refrigerators.• To learn and apply the second law of

thermodynamics• To study the Carnot engine: the most efficient

heat engine.• To overview entropy.

© 2016 Pearson Education, Inc.

© 2016 Pearson Education, Inc.

The Direction of a Thermodynamic Process• Heat flows spontaneously from a "hot" object to a "cold"

object.

• A process can be

• Spontaneous

• Non-spontaneous

• Reversible

• Irreversible

• In equilibrium

• Overall, there can be an increase or decrease in order.

• Devices can interconvert order/disorder/energy.

Fundamental laws of thermodynamicsZeroth Law Two systems that are each in

thermal equilibrium with a third system are in thermal equilibrium with each other.

First Law If Q is added and W is done then the U will change by:

ΔU = Q-W

Second LawEngine statement

It is impossible for any heat engine to undergo a cyclic process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work

Clicker - Questions

Which of the following actions is not even approximately reversible?

a) Jumping upward.

b) Bouncing on a pogo stick.

c) Skiing down an icy slope.

d) Swimming from one end of the pool to the other.

heat engines- cycle process

H

c

H

c

H Q

Q

C

Q

Q

We 11

Thermodynamical efficiency

Why does heat always flow from hotter to colder places and not in reverse?

One-way processes are derived by the second law of thermodynamics.

It uses the concept of entropy = quantitative measure of the degree of disorder

Heat engines, convert heat into work

Refrigerator, transport heat from colder to hotter object

Heat engine:Cyclic process with;

The ottocycle = gasoline engine

3 types of heat engines:1. Gasoline or Otto engine e = 56%2. Diesel engine e= 68%3. Carnot engine most efficient heat engine e= 90% for large temp difference

𝑟=𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛𝑟𝑎𝑡𝑖𝑜𝑛=𝑉𝑚𝑎𝑥

𝑉𝑚𝑖𝑛

=𝑝𝑖𝑠𝑡𝑜𝑛𝑑𝑜𝑤𝑛𝑝𝑖𝑠𝑡𝑜𝑛𝑢𝑝

≈8

For Diesel there is no fuel in the compression stroke and r can be large

Pre-igintion cannot occur since only hot air is present before the fuel is injected immediately before the power stroke

Line ab: At a air-gasoline mixture enters and is adiabatically compressed. At b ignition occurs.

Line bc: Adiabatic expansion

e=0.56 r=8 ottoe=0.70 r=15-20 Diesel

Second law of thermodynamics

Experimental evidence suggests that it is not possible to build an engine that convert heat completely into work.

No cyclic process can convert heat completely into work

Refrigerator Air conditioner

Refrigerator= heat engine in reverse

For a cyclic process and

Or because and

Performance coefficient of a refrigerator;[dimenionless]

It is a hot day in the city. Could you cool the place down by having everyone run their air conditioners with their window open?

A. Yes.B. No; the city would heat up.C. No; there would be no net change.

Clicker - Questions

Second law of thermodynamicsExperimental evidence suggest that it is impossible to build a heat engine that converts heat completely into work (with efficiency of 100%)

Engine statement

It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work with the system ending in the same state in which it began.

Refrigerator statement

It is impossible for any process to have as its sole result of the transfer of heat from a colder to a hotter object.

The conversion ofwork into heat is an irreversible process, therefore avoid all irreversible processesBottom line: every process of the cycle must be isothermal or adiabatic

Carnot Engine

Carnot engine=most efficient heat engine

Engine of maximum efficiency remain consistent with the second law of thermodynamics.

For Carnot cycle engine;

𝑒=1−𝑇 𝐶

𝑇𝐻

=𝑇𝐻−𝑇 𝐶

𝑇𝐻

Efficiency is the larger when the temperature difference is also larger.

The thermal efficiency formula is valid for which of the following heat engines? (There may be more than one correct choice)

A. Carnot engine.B. Otto engine.C. Diesel engine.D. Any other type of heat engine.

Clicker - Questions

Problem 16.2-1If a heat engine is 33% efficient, how much work can you get by putting 150J of heat, and how much heat do you waste doing each cycle?

Set up: , and , and

(wasted)

Problem 16.12For an Otto engine with a compression ratio of 7.50, you have your choice of using an Ideal monatomic or ideal diatomic gas. Which one would give greater efficiency?

Set up: . For a monoatomic ideal gas and for a diatomic gas

Solve: the monoatomic gas gives a larger e. For a monoatomic gas;

For a diatomic gas;

Problem 16.10In one cycle a freezer uses 785 J of electrical energy in order to remove 1750 J of heat From its freezer compartment at 10 F. a) what is the coefficient of performanceOf this freezer? b) how much heat does it expel into the room during this cycle?

Set up: For a refrigerator, the coefficient of performance is . and .

Solve: (a) (b)

Problem 16.15A refrigerator has a coefficient of performance of 2.10. Each cycle, it absorbs3.4 E4 J of heat from the cold reservoir. A) how much mechanical energy is required Each cycle to operate the refrigerator? B) During each cycle, how much heat is Discarded to the high-temp reservoir?

Set up: For a refrigerator, . , , and .

Solve: (a)(b)

Reflect: More heat is discarded to the high temperature reservoir than is absorbed from the cold reservoir.

The gasoline engine in a truck takes 2500J of heat and delivers 500J of mechanical work per cycle. Assume the heat of combustion

(a) What is the thermal efficiency?

(b) How much heat is discarded in each cycle?

(c) How much gasoline is burn in each cycle?,

(d) Assume the engine goes through 100cycles/second, what is the power output in watts?

(e) How much gasoline is burnt per second and per hour?

Per second:

Per hour:

Note: the density of gasoline Volume=

Example 16.1 Fuel consumption in a truck

𝑄𝐶=−2000 𝐽

Problem 16.21: Carnot engine

Consider the pV-diagram of the Carnot engine shown

a) If this engine is used as a heat engine, what is the direction of the cycle; clockwise or counter-clockwise?

Clockwise, because for a heat engine and are positive and is negative.

More positive work is done during ab and bc than the magnitude of the negative work done in cd and da. The net work done in the cycle is positive and equal to the area enclosed by the loop.

Problem 16.7

Set up: ca is at constant volume, ab has , and bc is at constant pressure. For a constant pressure process and gives

So, . For diatomic ideal . 1atm=1.013x105 Pa

(a) Find the pressure in point a

Solve: (a) , and . For adiabatic process .

(b) How much heat enters this gas per cycle?

Solve: (b) Heat enters the gas in process ca., since T increases.

(c) How much heat leaves this gas per cycle?

Solve: (c) Heat leaves the gas in process bc., since T decreases.

(d) How much work does this engine do per cycle?

Solve: (d)

(e) What is the thermal efficiency?

Solve: (e)

Reflect: We did not use the number of moles of the gas

Consider the pV-diagram of the heat engine that uses 0.25mol of an ideal gas with . The curved path ab is adiabatic.

Entropy and Disorder

Entropy provides a quantitative measure of disorder

Consider an infinitesimal isothermal expansion of an ideal gas, in that process we add heat Q, such that the temperature remains constant. Then all Q is converted to W.

The gas is in a more disorder state after the expansion since the molecules move in a larger volume and have more random mass in position.

Special most simple case

In a reversible isothermal process the entropy change unit []

Nature Favors Decrease in Order – Increase in Entropy

• The cream spontaneously mixes with the coffee, never the opposite.

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If you mix cold milk with hot coffee in an insulated Styrofoam cup, which of the following things happen? (There may be more than one correct answer)

A. The entropy of the milk increasesB. The entropy of the coffee decreases by the same amount that the

entropy of the milk increased.C. The net entropy of the coffee-milk mixture does not change,

because no heat was added to the system.D. The entropy of the coffee-milk mixture increases.

Clicker - Questions

Entropy and the Coffee

• Creamer does disperse in coffee, never the opposite.

• Rooms become dirty.

• A house of cards naturally will fall.

• A pressurized gas will spontaneously expand.

© 2016 Pearson Education, Inc.

An insulated box has a barrier that confines a gas to only one side of the box. The barrier springs a leak, allowing the gas to flow and occupy both sides of the box. Which statement best describes the entropy of this system?

A. The entropy is greater in the first state, with all the gas on one side of the box.

B. The entropy is greater in the second state, with all the gas on both sides of the box.

C. The entropy is same in both states, since no heat was added to the gas and its temperature did not change.

Clicker - Questions

© 2016 Pearson Education, Inc.

Free expansion=Irreversible processIsothermal expansion=reversible process

Q=0, W=0, U=0 in spite of this as we can see that entropy increases in a) and b)

∆𝑆=𝑄𝑇

Entropy change depends only on initial and final state. Since both processes have the same endpoints =same

Example 16.7

Example 16.4: Entropy change in melting ice

Compute the change in entropy of 1kg ice at 0oC when it is melted and converted to water at 0oC.

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