Physics 207: Lecture 27, Pg 1 Lecture 26Goals: Chapters 18, entropy and second law of thermodynamics Chapters 18, entropy and second law of thermodynamics.

Physics 207: Lecture 27, Pg 1

Lecture 26Goals:Goals:

• Chapters 18, entropy and second law of thermodynamicsChapters 18, entropy and second law of thermodynamics

• Chapter 19, heat engines and refrigeratorsChapter 19, heat engines and refrigerators

• No lab this week.

Sunduz Keles


Equipartition theorem

Things are more complicated when energy can be stored in other degrees of freedom of the system.

monatomic gas: translation

solids: translation+potential energy

diatomic molecules: translation+vibrations+rotations


Equipartition theorem

The thermal energy is equally divided among all possible energy modes (degrees of freedom). The average thermal energy is (1/2)kBT for each degree of freedom.

εavg=(3/2) kBT (monatomic gas)

εavg=(6/2) kBT (solids)

εavg=(5/2) kBT (diatomic molecules)

Note that if we have N particles:

Eth=(3/2)N kBT =(3/2)nRT (monatomic gas)

Eth=(6/2)N kBT =(6/2)nRT (solids)

Eth=(5/2)N kBT =(5/2)nRT (diatomic molecules)


Specific heat

Molar specific heats can be directly inferred from the thermal energy.

Eth=(6/2)N kBT =(6/2)nRT (solid)

ΔEth=(6/2)nRΔT=nCΔT

C=3R (solid)

The specific heat for a diatomic gas will be larger than the specific heat of a monatomic gas:

Cdiatomic=Cmonatomic+R


Second Law and Entropy

A perfume bottle breaks in the corner of a room. After some time, what would you expect?

A) B)


very unlikely

probability=(1/2)N

The probability for each particle to be on the left half is ½.


Second Law of thermodynamics

The entropy of an isolated system never decreases. It can only increase, or in equilibrium, remain constant.

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

Thermal energy is spontaneously transferred from a hotter system to a colder system.


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.)


Reversible vs IrreversibleBased on the above comments, which of the following

processes is not reversible?

A. Lowering a frictionless piston in a cylinder by placing a bag of sand on top of the piston.

B. Lifting the piston described in the previous statement by removing one tiny grain of sand at a time.


Heat Engines

Turning heat into work: Industrial revolution.

Volume

Pre

ssur

e

i

f


Key concepts

Work done by the system:

Wsystem=-Wexternal

Energy reservoir: An object that interacts with the system that is sufficiently large such that its temperature is almost constant.

QH: The amount of heat transferred to/from hot reservoirQC: The amount of heat transferred to/from cold reservoir


Energy-transfer diagram

Hot reservoir

Cold reservoir

QH

QC

Wout

cyclic systemΔEsystem=0 Wout=QH-QC


Thermal efficiency

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


What is the largest thermal efficiency that a heat engine can have?

A) η=2 B)η=1 C) η=1/2 D) η=0

What is the lowest thermal efficiency that a heat engine can have?

A) η=1/2 B)η=0 C) η=-1/2 D) η=-1


Refrigerators Devices that uses work to transfer heat from a colder object to a

hotter object.

Hot reservoir

Cold reservoir

QH

Win

Win+QC=QH

K=QC/WinQC


Is perfect engine possible?

Hot reservoir

Cold reservoir

QH1

Wout Win

QH2

QC

=QC

QH


Turbines: Brayton Cycle


Which of the following processes would have the largest work output per cycle?

V

P

V V

P PA) B) C)


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


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.


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

hot

coldcycleCarnot T

T1η

Physics 207: Lecture 27, Pg 1 Lecture 26Goals: Chapters 18, entropy and second law of thermodynamics Chapters 18, entropy and second law of thermodynamics.

Documents

b slide

b t diatomic molecules

b t monatomic gas avg

heat engines

f slide

b t solids avg

energy reservoir

w system