The density of copper is 8.2 g/cm3.

Find

A. The number of atoms in one cubic centimeter of copper.

B. The average distance between the atoms.

Repeat for silver (density 10.49 g/cm3).

Heat

• energy Q (1 cal = 4.182 Joule)– Energy transfer in a process due to

temperature differences– Q=mcT– Heat is not the only way to change

temperature• Specific heat?

Cold CupRoom temperature 20 Cm=150 g

Hot CoffeeT=90 CM=150 g

Where do you think the temperature of cup and coffee combined will end up after 30 s?

a) closer to 90Cb) at the average temperature 55C

c) closer to 20C

after 2 hours

Latent heat

-20

0

20

40

60

80

100

120

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00

time (min)

Te

mp

era

ture

(C

)

Pot of ice on a hot plate at constant heating

rate

Q1 Q2 Q3

No change in T Q changes T No change in T

Argon: internal energy versus temperature

-1800

-1300

-800

-300

200

0 20 40 60 80 100

temperature T (K)

energ

y (

kca

l/m

ol)

potential energykinetic energytotal energy

Solid liquid Ideal gas

Latent heat

• Energy transferred due to temperature differences with the environment

• Q=mL• Latent heat does not change temperature

of system (“hidden” = latent)• Latent heat: adds PE• Sensible heat: adds KE (changes T)

A New Years Custom

On New Years Eve, it is a custom in German-speaking regions to melt a small amount of lead and pour it into water. The created shapes are interpreted as symbolic for what the next year may bring to the pourer.

A bowl contains 300 g of water and 150 g of ice chips. How much molten lead needs to be added in order to melt all the ice?

Of the following choices, which can be used in order to

produce water of 50C by mixing?

(Consider equal amounts)

100C steam and 0C water

100C water and 0C water

100C water and 0C ice

100C steam and 0C ice

Transfer of heat

Why is the coffee cooling down?

Heat transfer processes

• Convection

• Radiation http://www.morris.umn.edu/~sboyd/index_files/Thermal%20images.htm

http://www.morris.umn.edu/~sboyd/weather/cloudthermal.htm

• Heat conduction

T

dQ TH k A

dt L

Coefficient of thermal conductivity

Heat conduction

T

dQ TH k A

dt L

k Coefficient of thermal conductivity

Aluminum 210 W/(m K)

Glass 0.9 W/(m K)

T1 T2 < T1

L

A

Water 0.58 W/(m K)

Air 0.026 W/(m K)

Q

Window

Find the heat lost to the environment through a window of

1.20m by 1.20m area during a winter night (12 h).

The indoor temperature is +20 C, while the outdoor

temperature is -20C.

a) The window consists of 15 mm of glass.

b) The window consists of two 5-mm panes with a gap of

5mm air in-between.

Dewar vessel

vacuum

Silvered walls

Styrofoam plug

Remove the ice build-up or not?

Two faculty members argue whether the ice should be removed from the lounge refrigerator or not in order to save energy.– A claims that the ice in the compartment provides enough thermal

mass to keep the contents cold. Therefore, one should retain the ice chunks.

– B claims that the ice prevents the function of the refrigerator since it covers the cooling pipes.

Who is right?

-10C

-25C -25C

-10C

k=205 W/mKk=1.6 W/mK, c=2100 J/kgK

Linear thermal expansion

T0, L0

L

T, L

oL T T

0L L 0 0L L T T

1611 10 osteel C

1612 10 oconcrete C

See table 12.2

Pontchartrain Causeway

Lake Pontchartrain is a large shallow brackish lake bordering New Orleans to the north. A 23-mile causeway bridge is leading over the lake.

The temperatures in winter drop to about 35F, while in summer the surface temperature of the bridge easily surpasses 120F.

Estimate the length difference of this concrete causeway between winter and summer.

Volume expansion

0 0V V T T

0 0 0L L L T T

Relation between volume expansion coefficient and linear expansion coefficient?

3

Causes of thermal expansion?

x

Potential energy of bond

Distance between two particles

Spring-like bonds

Equilibrium distance

Realistic bonds

Equilibrium distance

Asymmetric binding energyresults in thermal expansion of solids

Behavior of gases

Consider a cylinder filled with air. A piston is slowly being pushed to the left.

Assume, the gas is in thermal equilibrium with its surroundings.

When the volume of gas will become smaller, will the pressure1 increase?2 decrease?

3 stay the same?

290 K 290 K pV constBoyle’s Law

Isothermal process

Behavior of gases

Consider the same cylinder.The piston is free to move without friction (p=const).

A flame is slowly heating the air inside.When the temperature of the air increases, will the volume

1 increase?2 decrease?

3 stay the same?

P=1atmP=1atm .

Vconst

T

Charles’ Law

Isobaric process

Behavior of gases

Consider the same cylinder.The piston is fixed (V=const).

A flame is slowly heating the air inside.When the temperature of the air increases, will the pressure

1 increase?2 decrease?

3 stay the same?

pconst

T

Gay-Lussac’s Law

Isochoric process

Ideal gas law

pV nRT

8.314J

Rmol K

How many kg of air would we find in the auditorium at this time?

D=1.23 kg/m3

Phase diagrams of the ideal gas0

.00

.51

.01

.52

.0

0

50

10

0

15

0

molar volume (L/mol)

pre

ssu

re (

atm

)

200 K

500 K

800 K

0.0

0.5

1.0

1.5

2.0

0 200 400 600 800temperature (K)

pre

ssu

re (

atm

)

1000L/mol100L/mol50L/mol

0

50

100

150

0 200 400 600 800temperature (k)

mo

lar

volu

me

(L

/mo

l)

0.5 atm1 atm1.5 atm