16.1 Thermal Energy and Matter Chapter 16 Thermal Energy and Heat.
Short Version : 17. Thermal Behavior of Matter
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Transcript of Short Version : 17. Thermal Behavior of Matter
Short Version : 17. Thermal Behavior of Matter
17.1. Gases
The Ideal Gas Law:
A piston-cylinder system.
pV N k T
k = 1.381023 J / K = Boltzmann’s constant
N = number of molecules
AN n N
NA = 6.0221023 = Avaogadro’s number
= number of atoms in 12 g of 12C.
n = number of moles (mol)
pV n R T
AR N k = 8.314 J / K mol = Universal gas constant
All gases become ideal if sufficiently dilute.
Example 17.1. STP
What volume is occupied by 1.00 mol of an ideal gas
at standard temperature & pressure (STP),
where T = 0C, & p = 101.3 kPa = 1 atm?
pV n R T
n R TV
p
3 322.42 10 m 22.42 L
3
1.00 8.314 / 273.2
101.3 10
mol J K mol K
Pa
( last figure subject to round-off error )
Kinetic Theory of the Ideal Gas
Kinetic theory ( Newtonian mechanics ):
1.Gas consists of identical “point” molecules of mass m.
2. No interaction between molecules, except when they collide.
3. Random motion.
4. Collisions with wall are elastic.
Molecule i collides with right-hand wall (RHW).
Momentum transfer to wall is 2x i x ip m v
No intermolecular collision
Next collision with RHW occurs at2
ix i
Lt
v
Average force of i on RHW: ii
i
pF
t
2x im v
L
Fp
A i
iF
A 2
ix im v
A L
2x
ii
mv
V
2x
mp N v
V
22 1xx i
i
vvN
Random motion 2 2 2x y zv v v 21
3v 22 1
3 2pV N m v
2
3N K
Ideal gas law is recovered if21 3
2 2K m v k T T ~ K
in
out
Example 17.2. Air Molecule
Find K of a molecule in air at room temperature ( 20C = 293K),
& determine the speed of a N2 molecule with this energy.
3
2K k T 233
1.38 10 / 2932
J K K 216.07 10 J
2
272 14 1.66 10Nm u kg 264.65 10 kg
2 2 Kv
m
21
26
2 6.07 10
4.65 10
J
kg
5 2 22.61 10 /m s
2v v 511 /m s
3th
k Tv
mThermal speed:
Distribution of Molecular Speeds
Maxwell-Boltzmann Distribution: (elastic collisions between free particles)
High-E tail extends rapidly with T
chemical reaction easier at high T
cooling of liquid
( by escape of high-E molecules)
80 K
vth
300K
vth
2
2 exp2
mvn v C v
k T
0
n v dv N
Real Gases
Important corrections to the ideal gas model:
1.finite size of molecules available V reduced.
2.Attractive interaction between molecules (van der Waals forces) reduced P.
van der Waals equation
minimum volume
2
2
a nP V nb nRT
V
nRTP
V
2
2
nRT a nP
V nb V
17.2. Phase Changes
Phase changes take place at fixed T = TC until whole system is in the new phase.
( breaking / building bonds raises U but keeps K unchanged )
Heat of transformation L = energy per unit mass needed to change phase.
Lf = Heat of fusion ( solid liquid )
Lv = Heat of vaporization ( liquid gas )
Ls = Heat of sublimation ( solid gas )
Q L m
Water: 334 /fL kJ kg 80 /cal g
1 / /C cal g K
Same E to melt 1 g ice
or heat water by 80 C
Conceptual Example 17.1. Water Phases
T vs t for a block of ice, initially at - 20 C, that is
supplied with constant power under atmospheric P.
ice warming
melting
water warming
boiling
steam warming
You put a block of ice initially at - 20C in a pan on a hot stove with a constant power output,and heat it until it has melted, boiled, and evaporated.
Make a sketch of temperature versus time for this experiment.
Example 17.4. Enough Ice?
When 200 g of ice at 10 C are added to 1.0 kg of water at 15 C,
is there enough ice to cool the water to 0 C?
If so, how much ice is left in the mixture?
Q L m
1.0 4.184 / / 15waterQ kg kJ kg K C
Q m c T
Heat released to bring water down to 0 C
62.8 kJ
0.2 2.05 / / 10iceQ kg kJ kg K C Heat required to bring ice up to 0 C
4.1 kJ
0.2 334 /meltQ kg kJ kg
Heat required to bring ice up to 0 C
66.8 kJ more than enough ice
Ice needed: 62.8 4.1
334 /
kJm
kJ kg
0.176 kg ice left = 200 176 24g g g
Phase Diagrams
Phase diagram: P vs T
Sublimation: solid gas
e.g., dry ice ( s-CO2 )
AB: low P, s g
CD: medium P, s l g
EF: high P, s l / f
GH: medium T, l g
Caution: Phase transition doesn’t occur instantaneously
Triple point: s-l-g coexist
= 273.16K, 0.6 kPa for H2O
Solid
Gas
liquid
Melting
Sublimation
Boiling
C.P.
T.P.
壓力
TC
PC
Supercritical fluid : l-g indistinguishable
C.P. : Critical point
17.3. Thermal Expansion
Coefficient of volume expansion :
/V V
T
1 dV
V dT
Coefficient of linear expansion :
/L L
T
3
Prob. 69
Prob. 72
Example 17.5. Spilled Gasoline
A steel gas can holds 20 L at 10C.
It’s filled to the brim at 10C.
If the temperature is now increased to 25C, by how much does the can’s volume increase?
How much gas spills out?
Table 17.2: 6 112 10steel K 6 136 10steel K
5 195 10gas K
/V V
T
V V T
6 120 36 10 25 10canV L K C C 0.0108 L
5 120 95 10 25 10gasV L K C C 0.285 L
Spilled gas: 0.285 0.0108 0.275L L L
Thermal Expansion of Water
Reason: Ice crystal is open ice water
ice floats
max water occurs at 4C
At 1C5 14.8 10water K
At fixed T Tm , ice melts if P .
Application: skating.
> 0 < 0
Application: Aquatic Life & Lake Turnover
Anomalous behavior of ice-water makes aquatic life in freezing weather possible.
If deep enough, bottom water stays at 4C even when surface is iced over.
In a lake where bottom water stays at 4C year round,
surface & bottom water can mix (turnover) only in spring time when both are at 4 C.