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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