Chapter 12
Temperature and Heat
Chapter 13
The Transfer of Heat
Temperature
• Thermodynamics – branch of physics studying
thermal energy of systems
• Temperature (T), a scalar – measure of the thermal
(internal) energy of a system
• SI unit: K (Kelvin)
• Kelvin scale has a lower limit (absolute
zero) and has no upper limit
William Thomson
(Lord Kelvin)
(1824 - 1907)
Kelvin scale
• Kelvin scale is defined by the temperature of the
triple point of pure water
• Triple point – set of pressure and temperature
values at which solid, liquid, and gas phases can
coexist
• International convention:
T of the triple point of water is
T3  273.16 K
The zeroth law of thermodynamics
• If two (or more) bodies in contact don’t change their
internal energy with time, they are in thermal
equilibrium
• 0th law of thermodynamics: if bodies are in thermal
equilibrium, their temperatures are equal
Measuring temperature
• Temperature measurement principle: if bodies A and
B are each in thermal equilibrium with a third body C,
then A and B are in thermal equilibrium with each
other (and their temperatures are equal)
• The standard temperature for the Kelvin scale is
measured by the constant-volume gas thermometer
Constant-volume gas thermometer
P  P0  gh
T  CP
T3  CP3
P
T  T3
P3
P
 273.16 K 
P3
Celsius and Fahrenheit scales
• Celsius scale:
TC  T  273.15
• Fahrenheit scale:
9
TF  TC  32
5
Anders Cornelius
Celsius
(1701 - 1744)
Gabriel Daniel
Fahrenheit
(1686 - 1736)
Chapter 12
Problem 8
If a nonhuman civilization were to develop on Saturn’s largest moon, Titan, its
scientists might well devise a temperature scale based on the properties of
methane, which is much more abundant on the surface than water is. Methane
freezes at -182.6 °C on Titan, and boils at -155.2 °C. Taking the boiling point of
methane as 100.0 °M (degrees Methane) and its freezing point as 0 °M, what
temperature on the Methane scale corresponds to the absolute zero point of
the Kelvin scale?
Thermal expansion
• Thermal expansion: increase in size with an
increase of a temperature
• Linear expansion:
L
 T
L
• Volume expansion:
V
  T
V
  3
Thermal expansion
Chapter 12
Problem 21
A simple pendulum consists of a ball connected to one end of a thin brass wire.
The period of the pendulum is 2.0000 s. The temperature rises by 140 °C, and
the length of the wire increases. Determine the period of the heated pendulum.
Temperature and heat
• Heat (Q): energy transferred between a system and
its environment because of a temperature difference
that exists between them
• SI Unit: Joule
• Alternative unit: calorie (cal):
1 cal  4.1868 J
Absorption of heat
Q  cmT  cm(T f  Ti )
• Specific heat (c): heat capacity per unit mass
• Common states (phases) of matter: solid, liquid, gas
Q  Lm
• Latenet heat (L): the amount of energy per unit
mass transferred during a phase change (boiling,
condensation, melting, freezing, etc.)
Q
Q
Absorption of heat
Q
Q
Absorption of heat
Absorption of heat
Chapter 12
Problem 55
A rock of mass 0.20 kg falls from rest from a height of 15 m into a pail
containing 0.35 kg of water. The rock and water have the same initial
temperature. The specific heat capacity of the rock is 1840 J/(kg × C°). Ignore
the heat absorbed by the pail itself, and determine the rise in the temperature
of the rock and water.
Chapter 12
Problem 69
An unknown material has a normal melting/freezing point of -25.0 °C, and the
liquid phase has a specific heat capacity of 160 J/(kg × C°). One-tenth of a
kilogram of the solid at -25.0 °C is put into a 0.150-kg aluminum calorimeter cup
that contains 0.100 kg of glycerin. The temperature of the cup and the glycerin
is initially 27.0 °C. All the unknown material melts, and the final temperature at
equilibrium is 20.0 °C. The calorimeter neither loses energy to nor gains energy
from the external environment. What is the latent heat of fusion of the unknown
material?
Heat transfer mechanisms
• Thermal conduction
• Conduction rate:
Pcond
• Thermal resistance:
Th  Tc
Q
  kA
t
L
L
R
k
Thermal conductivity
• Conduction through a composite rod:
Pcond
ATh  Tc 

L1 / k1  L2 / k 2
ATh  Tc 

R1  R2
Heat transfer mechanisms
Chapter 13
Problem 15
A pot of water is boiling under one atmosphere of pressure. Assume that heat
enters the pot only through its bottom, which is copper and rests on a heating
element. In two minutes, the mass of water boiled away is m = 0.45 kg. The
radius of the pot bottom is R = 6.5 cm, and the thickness is L = 2.0 mm. What is
the temperature TE of the heating element in contact with the pot?
Heat transfer mechanisms
• Thermal radiation
• Radiation rate:
Emissivity
Prad  eAT
• Stefan-Boltzmann constant:
• Absorption rate:
4
  5.67 10 8W / m 2  K 4
Pabs  eAT
4
env
Pnet  Pabs  Prad
 eA(T
4
env
Josef Stefan
(1835-1893)
T )
4
Chapter 13
Problem 31
Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical
container (r = 0.30 m). The container is a perfect blackbody radiator. The
container is surrounded by a spherical shield whose temperature is 77 K. A
vacuum exists in the space between the container and the shield. The latent
heat of vaporization for helium is 2.1 × 104 J/kg. What mass of liquid helium
boils away through a venting valve in one hour?
Pnet  e A T 4  T04  4 R 2e T 4  T04

Q  mLv



Q
m
Lv
Pnet
Pnet t
4 R 2e T 4  T04 t
m
Lv


Q

t
Q  Pnet t

Lv
2
4
4
4  0.30 m  1 5.67 108 J/  s  m 2  K 4    77 K    4.2 K    3600 s 
m
 0.39 kg
4
2.110 J/kg
Heat transfer mechanisms
• Convection
Heat transfer mechanisms
Questions?