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Thermal Physics (Thermodynamics)
• Concerned with the concepts of thermal (or internal)
energy transfers between a system and its
environment and the resulting temperature
variations
– Temperature is central concept of thermodynamics
– Be careful not to trust your (subjective) senses to measure
temperature!
• Historically, the development of thermodynamics
paralleled the development of atomic theory
• Concerns itself with the physical and chemical
transformations of matter in all of its forms: solid,
liquid, and gas
– Temperature, heat flow, and internal energies will be
studied
Zeroth Law of Thermodynamics
• The flow of energy that occurs between 2 objects or
systems due to a temperature difference between
them is called heat flow
• Objects are in thermal contact if heat flow can take
place between them
• Thermal equilibrium exists when two objects in
thermal contact with each other cease to exchange
energy
• Definition of temperature relies on the zeroth law of
thermodynamics: If objects A and B are in thermal
equilibrium with a third object, C, then A and B are in
thermal contact with each other
Zeroth Law of Thermodynamics
• Less formal definition: Every body has a property
called temperature. When 2 bodies are in thermal
equilibrium, their temperatures are equal, and vice
versa
• Zeroth law used constantly in the lab
– If we want to know if 2 liquids have same temperature, we
measure temperature of each with a thermometer
– No need to bring them into thermal contact
• Zeroth law came to light only in 1930s, long after 1st
and 2nd laws of thermodynamics were established
Thermometers
• Thermometers are devices used to
measure the temperature of an object
or a system
– Example is mercury thermometer
• Make use of physical properties that
change with temperature
• Many physical properties can be used
–
–
–
–
–
–
volume of a liquid
length of a solid
pressure of a gas held at constant volume
volume of a gas held at constant pressure
electric resistance of a conductor
color of a very hot object
Temperature Scales
• Thermometers can be calibrated by placing them in
thermal contact with an environment that remains at
constant temperature
– Environment could be mixture of ice and water in thermal
equilibrium
– Also commonly used is water and steam in thermal
equilibrium
• An ear thermometer measures infrared radiation
from the eardrum – why is this useful?
• Celsius scale: Temp. of ice–water (water–steam)
mixture defined as 0°C (100°C)
– Freezing point vs. boiling point of water
– Distance between these 2 points divided into 100 equal
segments
Temperature Scales
• Fahrenheit scale: Most common scale used in the
U.S.
– Employs a smaller degree than Celsius scale
– Uses a different zero of temperature than Celsius scale
• Temperature of the freezing point of water is set at
32°F
• Temperature of the boiling point of water is set at
212°F
• 180 divisions between these 2 points
• Conversion between Celsius (TC) and Fahrenheit
(TF) temperatures:
9
9
o
TF  TC  32
TF  TC
5
5
Gas Thermometer
• Ideally, the readings of a thermometer
should not depend on material used
• Gas thermometer comes close to this
ideal
• Principle is that pressure of a gas at
constant volume increases with temperature
• Gas placed in constant-volume container and
pressure is measured (manometer in figure above)
– Calibrated by measuring pressure at 2 temperatures
• Temperature readings are nearly independent of the
gas
• Pressure varies with temperature when maintaining
a constant volume
Gas Thermometer
• If temperature measurements
are performed with gas in flask
at different starting pressures at
0°C, the data looks like the
graph at right:
• In each case, regardless of the gas used, the
curves extrapolate to the same temperature
(absolute zero) at zero pressure
• Gases liquefy and solidify at very low temperatures,
so we can’t actually observe this zero-pressure
condition
• The absolute-zero reference point forms basis of
Kelvin temperature scale
Kelvin Temperature Scale
• Named for British physicist Lord Kelvin (1824–1907)
• Units same as those on Celsius scale, but zero
point is shifted so that 0 K = –273.15°C:
TK  TC  273.15
• Modern definition (since 1954) of Kelvin scale
defined in terms of two points
• First point is absolute zero
• Second point is the triple point of water
– Triple point is the single point where water can exist as
solid, liquid, and gas
– Single temperature and pressure
– Occurs at 0.01°C and P = 4.58 mm Hg
– 1 K = 1/273.16 of temperature of triple point of water
Some Kelvin Temperatures and
Temperature Scale Comparisons
Thermal Expansion
• The thermal expansion of an object is a
consequence of the change in the
average separation between its
constituent atoms or molecules
• At ordinary temperatures, molecules
vibrate with a small amplitude
• As temperature increases, the amplitude
increases
– This causes the overall object as a whole to expand
• For relatively small changes in temperature, the
linear dimensions of object change according to:
L  aL0 T
– Coefficient of linear expansion, a, depends on the material
(see Table 10.1)
– These are average coefficients (they can vary with
temperature)
Thermal Expansion
• Since the linear dimensions of an object change with
temperature, there is also a change in surface area:
A  gA0 T
(g = 2a = coefficient of area expansion)
• And a change in volume:
V  bV0 T
(b = 3a = coefficient of volume expansion for
solids; for fluids, see Table 10.1)
– g  2a and b  3a only if a is the same in all directions
• Many applications of thermal expansion
– Pyrex glass
– Expansion joints in bridges and buildings
– Rising sea levels due to ocean warming
Thermal Expansion
• Thermostats
– Bimetallic strips in thermostats (2 metals expand differently)
(abrass > asteel)
CQ1: The Statue of Liberty is 93 m tall on a
summer morning when the temperature is 20°C.
If the temperature of the statue rises from 20°C
to 30°C, what is the order of magnitude of the
statue’s increase in height? Choose the best
estimate, treating the statue as though it were
solid copper (a = 17 × 10–6 °C–1 ).
A)
B)
C)
D)
E)
0.1 mm
1 mm
1 cm
10 cm
1m
Example Problem #10.23
The band in the figure at right is stainless steel
(coefficient of linear expansion a = 17.3  10–6 °C–1 ;
Young’s modulus Y = 18  1010 N/m2). It is
essentially circular with an initial mean radius of 5.0
mm, a height of 4.0 mm, and a thickness of 0.50
mm. If the band just fits snugly over the tooth when
heated to a temperature of 80°C, what is the
tension in the band when it cools to a temperature
of 37°C?
Solution (details given in class):
2.7  102 N
Thermal Expansion of Water
• As the temperature of water decreases from 4ºC to
0ºC, it expands and its density decreases
• Above 4ºC, water expands with increasing
temperature, typical of other liquids and materials
• Maximum density of water is 1000 kg/m3 at 4ºC
• This unusual behavior explains why:
– ice humps up in the middle of the compartments in an ice
cube tray
– a lake freezes slowly from the
top down (important for animal
and plant life!)
– water pipes can burst in the
winter
Ideal Gas
• A gas does not have a fixed volume or pressure
• In a container, the gas expands to fill the container
• Most gases at room temperature and pressure
behave approximately as an ideal gas (one in which
there is simple relationship between P, V, and T)
• Characteristics of ideal gas:
– Collection of atoms or molecules that move randomly
– Exert no long-range force on one another
– Occupy a negligible fraction of the volume of their
container
• Understanding ideal gases is useful because all real
gases approach an ideal gas at low enough densities
(when molecules are far enough apart that they do
not interact with each other)
Ideal Gas
• It’s convenient to express the amount of gas in a
given volume in terms of the number of moles, n:
mass
n
molar mass
• One mole is the amount of the substance that
contains as many atoms as there are atoms in
12 g of the carbon–12 isotope
– 1 mol of a substance contains the same number of atoms
as in 1 mol of any other substance
• The number of atoms in one mole is called
Avogadro’s Number = NA = 6.02 1023 atoms/mol
• We can use this number to calculate the mass of an
individual atom: m  molar mass
atom
NA
Ideal Gas Law
• Boyle’s Law
– At a constant temperature, pressure is inversely
proportional to the volume
• Charles’ Law
– At a constant pressure, the temperature is directly
proportional to the volume
• Gay-Lussac’s Law
Ideal Gas Properties
– At a constant volume, the pressure is directly
proportional to the temperature
• These 3 laws are summarized by the Ideal Gas Law:
PV  nRT
(P = absolute pressure, T = temp. in Kelvin)
– R = universal gas constant = 8.31 J/molK
= 0.0821 Latm/molK
(note that if n = constant, PV/T = constant)
CQ2: If the volume of an ideal gas is
doubled while its temperature is
quadrupled, what happens to the pressure
of the gas?
A) It remains the same.
B) It decreases by a factor of 2.
C) It decreases by a factor of 4.
D) It increases by a factor of 2.
E) It increases by a factor of 4.
Example Problem #10.32
A tank having a volume of 0.100 m3 contains
helium gas at 150 atm. How many balloons can
the tank blow up if each filled balloon is a
sphere 0.300 m in diameter at an absolute
pressure of 1.20 atm?
Solution (details given in class):
884 balloons
CQ3: Interactive Example Problem #10.35
A weather balloon is designed to expand to a
maximum radius of 20 m at its working
altitude, where the air pressure is 0.030 atm
and the temperature is 200 K. If the balloon
is filled at atmospheric pressure and 300 K,
what is its radius at liftoff?
A)
B)
C)
D)
E)
4.2 m
7.1 m
18 m
49 m
358 m