Chapter 11: Thermal Physics
Temperature:
A quantitative measure of “hot” or “cold”
Operational definition: Temperature is what is measured by a thermometer.
mercury thermometer
constant volume gas thermometer
bimetallic strip
All involve measurable physical changes in response to temperature changes.
Temperature Scales
water freezes
water boils
Fahrenheit
32º
212º
Celsius
0º
100º
TF = 9/5 TC + 32
Examples: What Fahrenheit temperature corresponds to 37.0 ºC? to 20.0 ºC? What Celsius
temperature corresponds to 86 ºF?
Phys 250 Ch10 p1
Gas thermometer and absolute temperature scales
Constant volume gas thermometer
pressure changes indicate temperature changes
At low densities
Dp DT
All gases have same x-intercept
p = 0 at TC = -273ºC
TF = -460ºF
Absolute temperature scales:
T = 0 when p = 0
Kelvin
TK = TC + 273
Rankine
TR = TF + 460
Phys 250 Ch10 p2
p
TC = -273ºC
T (Celsius)
TC = 0ºC
Thermal Expansion
A change in temperature causes a change in length in a solid object. Usually,
change in length DL
is proportional to change in temperature, DT
is proportional to original length, L0
depends upon type of material
DL  L0 DT
L0
DL
 = Coefficient of Linear Expansion (sometime a)
DL 1
Determine  experimentally:  
L0 DT
L  L0  DL  L0 (1  L0 (T - T0 ))
Phys 250 Ch10 p3
Substance
Aluminum
Copper
Linear Coefficien t Volume Coefficien t
2.4 10-5 / C
7.2 10-5 / C
1.7
5.1
Silver
2.0
6.0
Quartz
Steel
0.05
1.2
0.15
3.6
Glass
0.9
2.7
water
-
21
Example: The center span of the Verrazano-Narrows Bridge is 1300 m long. Assuming the
bridge is made of steel, how much expansion will there be for a temperature range of 120ºC?
Phys 250 Ch10 p4
Example: A copper hot-water pipe is 10.0 m long when installed on a day when the
temperature is 10ºC. How long is the pipe when it carries hot water at 60ºC if the pipe
is free to expand?
Phys 250 Ch10 p5
Volume expansion (of solids and liquids)
linear expansion in 3-D!
A change in temperature causes a change in volume. The change in volume DV
is proportional to change in temperature, DT
is proportional to original length, V0
depends upon type of material
DV  V0 DT
 = Coefficient of volume expansion
for solids, = 3
How are voids (holes) in materials affected by changing temperatures?
Phys 250 Ch10 p6
Voids in materials expand and contract as if they were made of the material.
Example: How much water overflows from a 1 liter glass beaker filled to the brim with
water at 20°C when beaker and contents are both heated to 95° C? Use average value
of  = 525E-6/ºC
Phys 250 Ch10 p7
What is heat?
One thing which is transferred between two systems initially at different temperatures as
they come to thermal equilibrium.
Heat is energy which is transferred solely because of temperature differences.
Heat addition to a system can cause temperature changes.
“Mechanical Equivalent” of Heat: 1 calorie = 4.187 joules
Heat Units, defined in terms of the properties of water
calorie: the energy required to raise the temperature of 1 gram of water by 1 ºC (4.187 J)
kilocalorie: a.k.a. Calorie a.k.a. dietetic calorie = 1000 calories (4187 J)
British Thermal Unit: the energy required to raise the temperature of 1 pound of water by
1 ºF (1060 J)
Example: A candy bar has 200 dietetic Calories. How many time must a 10 kg weight be
lifted through a height of 2m to work off the candy bar if the human body is 10% efficient at
converting calories to mechanical energy?
Phys 250 Ch10 p8
Calorimetry
For a sample of a substance that does not undergo a change of state:
Heat added: Q is proportional to
DT = Tf- Ti , the change in temperature
m, the mass of the sample
Q = mc DT
c is the material’s specific heat
In a closed system (hot object interacts with cool object)
heat gained by cool object(+) + heat lost by hot object(-) =0
Substance kJ/(kg ºC)
Water
4.19
kcal/(kg ºC)
cal/(g ºC)
1.00
Glass
.39
.093
Ice
2.09
0.50
Copper
0.39
0.093
Air
0.70
0.17
Phys 250 Ch10 p9
Example: A Styrofoam cup of negligible heat capacity contains 150 g of water at 10ºC.
If you add 100 g of water at 85ºC, what is the final temperature of the mixture?
Phys 250 Ch10 p10
Example: A 74 g metal block is heated to 90ºC. It is then submerged in 300 g of water
at 10ºC. The final temperature is 14ºC. What is the specific heat of the material?
Phys 250 Ch10 p11
Phase Changes
Phase of Matter: solid, liquid, gas etc.
Phase Change (Phase Transition)
solid -> liquid (melting), liquid -> gas (boiling)
heat added (or removed) without a change in temperature (reversible process)
Two states of matter coexist (in equilibrium) only at the transition temperature
amount of heat proportional to mass of substance
Q = mL
L is the Latent heat
Water:
Latent heat of fusion is the energy cost to convert a unit mass of ice at the melting
temperature to a unit mass of water at the melting temperature.
Lf = 80 kcal/kg = 334 kJ/kg
Latent heat of vaporization is the energy cost to convert a unit mass of water at the
boiling temperature to a unit mass of steam at the boiling temperature.
Lv = 540 kcal/kg = 2260 kJ/kg
T
steam
water-steam
ice-water
Phys 250 Ch10 p12
ice
water
Q
Water:
Latent heat of fusion is the energy cost to convert a unit mass of ice at the melting
temperature to a unit mass of water at the melting temperature.
Lf = 80 kcal/kg = 334 kJ/kg
Latent heat of vaporization is the energy cost to convert a unit mass of water at the boiling
temperature to a unit mass of steam at the boiling temperature.
Lf = 540 kcal/kg = 2260 kJ/kg
T
steam
water-steam
ice-water
ice
Phys 250 Ch10 p13
water
Q
Example: A 105 g copper calorimeter contains 307 g of water at 23ºC. If 52 g of ice at
0ºC is added to the calorimeter, what is the final temperature of the system?
Example: A 105 g copper calorimeter contains 307 g of water at 23ºC. If 95 g of ice at
0ºC is added to the calorimeter, what is the final temperature of the system?
Phys 250 Ch10 p14
Mechanisms of Heat Transfer
Conduction
Convection (Natural vs Forced)
Radiation (Electromagnetic Waves)
Conduction:
No bulk motion of matter
Microscopic transfer of kinetic energy to adjacent regions
Because KE of electrons in a conductor “easily” transported from one region to
another, good electrical conductors are generally good thermal conductors
Rate of heat flow:
DQ
T -T
 KA 2 1
Dt
L
K  Thermal Conductivi ty
T2 - T1
 Temperatur e Gradient
L
L
R
" R - value"
K
Phys 250 Ch10 p15
T2
T1
H
A
Example: A Styrofoam cooler has a surface area of 0.50 m2 and an average thickness of
2.0 cm. How long will it take for 1.5 kg of ice to melt if the outside temperature is
30ºC? use K=0.030 W/(m ºC)
Phys 250 Ch10 p16
Convection
Bulk motion of fluid (forced or natural)
chief mechanism of heat lost under most situations
COMPLEX!!!
Depends upon fluid and geometry
Q
 hA(TH - TC )
t
h = skin coefficient; depends upon temperatures, fluid, geometry, etc.
H
Radiation (electromagnetic waves)
= “Blackbody” Radiation
Stephan- Boltsmann Law:
P  DQ / DT  eAT 4
 = 5.6705 10-8 W m 2  K 4  Stephan - Boltzmann Constant
e = emissivity (0  e < 1)
Pnet  DQ / DT  eA(T 4 - Ts )
4
Phys 250 Ch10 p17
Radiation (electromagnetic waves)
=“Blackbody” Radiation
I
Stephan- Boltsmann Law:
l
P  DQ / DT  eAT 4
 = 5.6705 10-8 W m 2  K 4  Stephan - Boltzmann Constant
e = emissivity (0  e < 1)
Phys 250 Ch10 p18
Example: A patient waiting to be seen by his physician is asked to remove all his clothes in a
room that is at 16ºC. Calculate the rate of heat loss by radiation given that the patient has a
temperature of 34ºC and his surface area is 1.6 m2. Assume an emissivity of 0.80.
Phys 250 Ch10 p19