Paperwork

• Mastering Physics

• Course # DRKIDD880131

• Has online book access

• Put up two assignments– Real & practice– Let me know if practice is useful– Other study areas appear useful.

Schedule Short Term

• Today – Work out Exercise #2

• Friday – Chapter 18 Lecture

• Monday – Off

• Tuesday – Lab #1– Copyworks– Quiz#1

• Wed HMWK due 11pm

Problem Solving Ch. 17

• Exercises– Toss in shark infested waters & see how you

swim…

– #1 of special interest to physics majors. Will let you work it out, ask for help if you like.

– #2 – Let’s do it now

Temperature vs. Energy Plot

Exercises

• 2. Heat transfer– How many grams of boiling gold would it take

to boil 100 grams of water held at room temperature (say 300K)?

– How much boiling water would it take to melt 10 grams of gold?

– Let’s Simplify Problem a little bit

Exercises

• 2. Heat transfer– A. What is the least amount of molten gold that it

would take to boil off 100 grams of water held at room temperature (say 300K)? The gold is at a temperature just above the melting point.

– B. How much boiling water would it take to melt 10 grams of gold?

– Now we don’t have to find the heat capacity of molten gold…

Equation?

• Equation relating Heat to Temp?

• Equation for relating heat to boiling/melt?

What do we need to know?

• A. What is the least amount of molten gold that it would take to boil off 100 grams of water held at room temperature (say 300K)? The gold is at a temperature just above the melting point.

• What type of problem is this?• What constants do we need?• Heat capacity of gold ~ 0.1 J/(g K)• Heat of fusion of gold ~ 65 J/g• Melting Point of gold ~ 1300 K• Heat capacity of water ~ 4 J/(g K)• Heat of vaporization of water ~ 2000 J/g

• Notice it takes a lot more energy to raise the temperature of water than gold. Insight into different types of solids? Metals, Insulators, etc…

Have Constants, Now What?

• A. What is the least amount of molten gold that it would take to boil off 100 grams of water held at room temperature (say 300K)? The gold is at a temperature just above the melting point.

• Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Have Constants, Now What?

• A. What is the least amount of molten gold that it would take to boil off 100 grams of water held at room temperature (say 300K)? The gold is at a temperature just above the melting point.

• Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass Heat

Constants Constants Heat

Initial Temp Init. Temp Final Temp Final Temp

Just from Problem itselfWhat can we figure out fast?

Have Constants, Now What?

Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass Heat

Constants Constants Heat

Initial Temp Init. Temp Final Temp Final Temp

How does final temp of gold relate to water?How does change in heat for gold relate to water?

Have Constants, Now What?

Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass Heat

Constants Constants Heat

Initial Temp Init. Temp Final Temp Final Temp

How does final temp of gold relate to water? Both 100oC How does change in heat for gold relate to water? Heat from Au = Heat into H20

Have Constants, Now What?

Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass

Constants Constants Heat (Same for Both)

Initial Temp Init. Temp

Final Temp Final Temp

How does final temp of gold relate to water? Both 100oC How does change in heat for gold relate to water? Heat from Au = Heat into H20

Two unknowns, need two equations.Notice we know everything about water…

To Solve

Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass

Constants Constants Heat (Same for Both)

Initial Temp Init. Temp

Final Temp Final Temp

Know everything about H20. Heat into H20 = Heat to raise water from RT to 100oC + Heat of vapor. for 100gHave constants, plug in and solve

To Solve

Determine what we know. Make Table of parameters.

Known Unknown

Gold Water Gold Water

Mass Mass

Constants Constants Heat (Same for Both)

Initial Temp Init. Temp

Final Temp Final Temp

Know everything about H20. Heat into H20 = Heat to raise water from RT to 100oC + Heat of vapor. for 100gHave constants, plug in and solveSet up similar equation for gold.Heat out of Au = Heat to fuse gold into a solid + heat to lower temp to 100oCMass is unknown variable, but have total heat (Same as found for H20)

Part B

• How much boiling water would it take to melt 10 grams of gold?

• What is equilibrium temperature?

• Melting point of gold?

Add some Calc

• Real materials, heat capacity not a constant. Depends on Temperature

• For gold say:• c ~ (0.1 + 0.001T) J/(g K)

dQ mcdT

Add some Calc

• c ~ (0.1 + 0.001T) J/(g K)

0

FT

T

Q mc dT

dQ mcdT

If mass is equal to 10 grams, how much heat is needed to raise the temperature from 100oC to 300oC?

Strategy

• c ~ (0.1 + 0.001T) J/(g K)

0 0

F FQ T

Q T

Q dQ mc dT

dQ mcdT

If mass is equal to 10 grams, how much heat is needed to raise the temperature from 100oC to 300oC?

Does m depend on T?

Strategy

• c ~ (0.1 + 0.001T) J/(g K)

0

FT

T

Q m c dT

dQ mcdT

If mass is equal to 10 grams, how much heat is needed to raise the temperature from 100oC to 300oC?

Now what?

Strategy

• c ~ (0.1 + 0.001T) J/(g K)

0

0.1 0.001FT

T

Q m T dT

dQ mcdT

If mass is equal to 10 grams, how much heat is needed to raise the temperature from 100oC to 300oC?

Now integrate and be done with it.

Strategy

• c ~ (0.1 + 0.001T) J/(g K)

0

0

2

2 2

0.1 0.001

0.1 0.0012

0.0010.1 300 100 300 100

2

F

F

T

T

T

T

Q m T dT

TQ m T

Q m

dQ mcdT

If mass is equal to 10 grams, how much heat is needed to raise the temperature from 100oC to 300oC?Now integrate and be done with it.

Schedule Short Term

• Today – Work out Exercise #2

• Friday – Chapter 18 Lecture

• Monday – Off

• Tuesday – Lab #1– Copyworks– Quiz#1

• Wed HMWK due 11pm