Quiz 7 8:30-8:50am TODAYHave your calculator ready.

Cell phone calculator NOT allowed.Closed book

Quiz 3 Re-evaluation Request Due this Thursday, 2/28.Quiz 4 Re-evaluation Request Due next Thursday, 3/6.

Turn in you original Quiz along with the Re-evaluation Request Form. Note: It is possible for your grade to be lowered after the re-evaluation.

Quiz 4 rubrics posted on the website. Quiz 4 info (average score, grades) will be posted this afternoon.Quiz 5,6 graded, grades being recorded.

Next lecture March 4Quiz 8 (Last Quiz!) will cover the material from today’s lecture and material from DLM12 and 13, excluding FNTs for DLM14.

Measuring Heat capacityMeasuring Heat capacity

ThermometerStirring rod

Heating element

Substance of interest

Insulating material

All measurements at 25 Cunless listed otherwise

(-1

00

C)

(0C

)

All measurements at 25 Cunless listed otherwise

(-1

00

C)

(0C

)

All measurements at 25 Cunless listed otherwise

(-1

00

C)

(0C

)

All measurements at 25 Cunless listed otherwise

(-1

00

C)

(0C

)

kBNA = R = 8.31 J/Kmole : Gas constant or Ideal gas constant

kB(Boltzman constant) = 1.38 x 10 -23 Joule/Kelvin

NA(Avogadro’s number) = 6.02 x 1023

6 modes

All measurements at 25 Cunless listed otherwise

(-1

00

C)

(0C

)

kBNA = R = 8.31 J/moleK : Gas constant or Ideal gas constant

kB(Boltzmann constant) = 1.38 x 10-23 Joule/Kelvin

NA(Avogadro’s number) = 6.02 x 1023

All measurements at 25 Cunless listed otherwise

All measurements at 25 Cunless listed otherwise

6 modes

All measurements at 25 Cunless listed otherwise

For polyatomic substances , the values of molar specific heat

of liquids are greater than the values for solids.

Limitation of our model…For monatomic substances, the value of molar specific

heat of liquids is similarto the values for solids.

Our model works well here!

(10

0 C

)

All measurements at 25 Cunless listed otherwise

(50

0 C

)

diatomic(no vibrations)

(10

0 C

)

All measurements at 25 Cunless listed otherwise

(50

0 C

)

monatomic

diatomic(no vibrations)

(10

0 C

)

All measurements at 25 Cunless listed otherwise

(50

0 C

)

monatomic

Oops! What’s going on??!

The discrepancy explained…

Closed box of gas Open box of gas

The discrepancy explained…

Closed box of gas Open box of gas

Closed box: all heat goes into the gas’s energy

Open box: Some heat goes into pushing air out of the way

The discrepancy explained…

Closed box of gas Open box of gas

Closed box: all heat goes into the gas’s energy

Open box: Some heat goes into pushing air out of the way

CV measurement

CP measurement

The discrepancy explained…

Closed box of gas Open box of gas

Closed box: all heat goes into the gas’s energy

Open box: Some heat goes into pushing air out of the way

CV measurement

CP measurement

Question

So then does it takeMore energy to raise the

Temperature of

Closed box of gasOr

Open box of gas?

(10

0 C

)

All measurements at 25 Cunless listed otherwise

(50

0 C

)

monatomic

Whew, Now that makes sense.

diatomic(no vibrations)

(10

0 C

)

All measurements at 25 Cunless listed otherwise

(50

0 C

)

monatomic

Whew, Now that makes sense.

“Constant volume” “Constant pressure”

“Process” seems to matter… => Chapter 4 Models of Thermodynamics

(definition of heat capacity)

In this example of thermal phenomena (i.e.,measuring heat capacity) ,

• Equipartition tells us that each (active) mode has the same amount of energy, and that the temperature is the measure of energy per mode

• Our mode counting works well for solids and gasses. For gasses, we need to distinguish between work and heat carefully (Chapter 4).

• Our mode counting does not work well for liquids.

Summary of Equipartition of EnergySummary of Equipartition of Energy

What is Thermodynamics?What is Thermodynamics?

Sadi Carnot (1796-1832)Father of Thermodynamics

James Joule

(1818-1889)

Lord Kelvin

(1824-1907)

In a nutshell, we study the transfer of energy between systems and how the energy instills movement, i.e., how the system responds.

Ex. If we heat something,it expands.

• Carefully distinguish between heat and work• Learn what a state function is• Think about things that depend on the process, and ask about

processes. (e.g. ice melts/water freeze, fry egg) Why doesn’t the fried egg turn into raw egg again?

Why can carbon exist as a diamond as well as graphite but not ice and vapor?

State functions

Depends only on properties of the system at a particular time

Work, heat

LHS: depends only on i and f

Q,W depend on process between i and f

Not a property of a particular object Instead a property of a particular process

or “way of getting from the initial state to the final state”

Ex. Ethermal of a gas For an ideal gas, Ethermal depends only on * Temperature * Number of modes

Remember conservation of energy?

∆U : Internal energyEnergy associated with the atoms/molecules inside the body Of material

A comment Remember conservation of energy?

∆Etotal must include all changes of energy associated with the system…

∆Etotal = ∆Ethermal + ∆Ebond + ∆Eatomic + ∆Enuclear + ∆Emechanical

Energy associated with the motion of a body as a whole

So then, if there’s no change in ∆Emechanical

∆ U

First law of Thermodynamics

• Depend only on what the object is doing at the time.

• Change in state function depends only on start and end points.

• Examples:

T, P, V, modes, bonds, mass, position, KE, PE...

State functions

• Depend on the process.

• Not a property of an object

• Examples:Q, W,

learning , ......

Process- dependent

Work

initial

initial

finalfina

l

P

VV

P

Along any given segment

initial

final

P

V

First section: W1 < 0 (volume expands)Second section: W2 = 0 (volume constant)Third section: W3 > 0 (volume contracts)

Work

initial

final

P

V

Here are two separate processes acting on two different ideal gasses. Which one has a greater magnitude of work? The initial and final points are the same.

initial

finalP

V

A) Magnitude of work in top process greaterB) Magnitude of work in lower process greaterC) Both the sameD) Need more info about the gasses.

initial

final

P

V

Is the work done in the process to the right positive or negative?

A) PositiveB) NegativeC) Zero D) Impossible to tell.

Heat and the first law of Thermodynamics

initial

final

V

P

We can read work directly off this graph(i.e. don’t need to know anything about modes, U,

T, etc.)

If we know something about the gas, we can figure out Ui, Uf and Uf - Ui

initial

final

V

P

Heat and the first law of Thermodynamics

Example5 moles of a monatomic gas has its pressure increased from 105 Pa to 1.5x105 Pa. This process occurs at a constant volume of 0.1 m3. Determine: * work, * change in internal energy * heat involved in this process.

initial

final

P

V

Heat depends on the process

Work depends on the process

only depends on initial and final

W = 0 for all constant volume processes

A comment

Enthalpy

Is a state function:- U depends only on state of system- P depends only on state of system- V depends only on state of system

=> H depends only on state of system

(Hess’s law)

Who cares?!?!

initial

final

P

V

initial

final

P

V

W = 0

Constant volume Constant pressure

Note: nothing about gasses used - works for solids and liquids too!

Enthalpy

*Derivation in P.84

Below boiling point

Freezing of modes: Nitrogen

(per molecule)

(per molecule)

Below boiling point

California temps

Freezing of modes: Nitrogen

(per molecule)

(per molecule)

Closed Book

Don’t forget to fill in your DL

section number!