Download Lecture 26 - PhysicsGivesYouWings

Physics 103
May 2, 2017
Lecture 26
Temperature (Ch. 19)
Thermal Expansion (Ch. 19)
Ideal Gas (Ch. 19)
Announcements
• SIRI = Student Independent Research Internship
– Unpaid internship during the Fall semester.
– Offered through the Jet Propulsion Laboratory (JPL).
• Application process:
– Submit application to [email protected] by
4May2017.
• For more information, visit:
http://physicsgivesyouwings.wikispaces.com/SIRI+Program
https://www.jpl.nasa.gov/edu/intern/apply/student-independent-research-intern/
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Thermal Equilibrium
• Two objects placed in physical contact may
exchange energy.
– As the molecules of one object collide with the
molecules of the other object, kinetic energy is
exchanged between them.
• Two objects are said to be in thermal equilibrium
if no energy is exchanged between them when
brought into physical contact.
– Different from mechanical equilibrium:
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Zeroth Law
• Zeroth Law of Thermodynamics (Law of Thermal
Equilibrium): If objects A and C are separately in
thermal equilibrium with a third object B, then A
and C are in thermal equilibrium with each other.
B
A
Ther. Equil.
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Temperature
• Temperature is that property which determines if
two objects are in thermal equilibrium.
• Consider any two objects A and B:
– If
– If
, then A and B are in ther. equilibrium.
, then A and B are not in ther. equilibrium.
• The three most common are the scales invented
by Fahrenheit, Celsius and Kelvin.
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Temperature Scales
• Fahrenheit (1724):
– Freezing point of brine (water + salt) is set to 0.
– Human body temperature is set to 96, but was later
adjusted to 98.6.
• Celsius (1742):
– Freezing point of water is set to 0.
– Boiling point of water is set to 100.
• Kelvin (1848):
– “Infinite cold” is set to zero, known as
absolute zero.
– Triple point of water is set to 273.16.
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Temperature Conversions
• Converting from Celsius to
Fahrenheit:
– One increment in Fahrenheit’s scale is
equal to
of one increment in
Celsius’ scale.
• Converting from Celsius to Kelvin:
– One increment in Kelvin’s scale is
equal to one increment in Celsius’
scale.
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Comparison of Temperature Scales
• All three temperature scales have different zeros.
• Celsius and Kelvin have the same units.
Fahrenheit:
0
1
Celsius:
Kelvin:
2
0 1
0 1
2
3
4
5
6
3
4
2
3
4
5
7
8
9
10
6
5
7
8
9
10
• Temperature difference:
• Temperature ratio:
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Thermal Expansion
• Length of a solid object changes with temperature:
Substance:
Invar
Pyrex Glass
Ordinary Glass
Aluminum
:
• Volume of gasses, liquids and solids changes with
temperature:
Substance:
Air (
)
Alcohol
Mercury
Gasoline
:
• For solids:
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Practice Problem
Two concrete spans of a
-meterlong bridge are placed end to end so
that no room is allowed for
expansion. If a temperature increase
of
occurs, what is the height
to which the spans rise when they
buckle? You may use
for concrete.
For each piece of concrete:
The rise is:
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Thermo vs Stat Mech
• Thermodynamics is the study of how heat and
temperature affect the behavior of substances.
• Statistical mechanics is the study of the motion
of a large number of particles.
• After the 1890s, it became increasingly obvious
that fluids are made of discrete units, i.e. atoms
or molecules.
– So thermodynamics was gradually replaced by
statistical mechanics.
– The ideal gas model will be our primary example.
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Ideal Gas
• An ideal gas is a collection of identical, weaklyinteracting particles confined to volume with
total energy .
– “Weakly-interacting” means no long-range forces
such as gravity or electric force; only contact forces.
– Particles obey the laws of classical mechanics, such as
Newton’s laws of motion and energy conservation.
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Boyle’s Law
• Consider a cylinder filled with a
fixed quantity of ideal gas:
– Volume of gas:
– Pressure of gas:
– Temperature of gas:
• Suppose is kept constant. If is
increased, what happens to ?
Boyle’s Law (1662)
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Charles’s Law
• Consider a cylinder filled with a
fixed quantity of ideal gas:
– Volume of gas:
– Pressure of gas:
– Temperature of gas:
• Suppose is kept constant. If is
increased, what happens to ?
Charles’s Law (1780)
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Gay-Lussac’s Law
• Consider a cylinder filled with a
fixed quantity of ideal gas:
– Volume of gas:
– Pressure of gas:
– Temperature of gas:
• Suppose is kept constant. If is
increased, what happens to ?
Gay-Lussac’s Law (1802)
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Ideal Gas Law
• Can the three laws be unified into one equation?
,
Boyle’s Law
,
Charles’s Law
Gay-Lussac’s Law
• The ideal gas law unifies the three laws:
–
–
is the number of molecules.
is known as
the Boltzmann constant.
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Ideal Gas Law (cont.)
• The ideal gas law is also expressed as:
–
–
is the number of moles of gas.
is known as the gas constant.
• Avogadro’s number:
• 1 mole of CO2
molecules of CO2
molecules CO2
• Number of moles and molecules:
• Boltzmann and gas constants:
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Practice Problem
A spray can with volume
contains ideal gas at temperature
and pressure
(
).
a) How many moles and how many molecules
of gas does the spray can contain?
Must convert to Kelvin:
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Practice Problem (cont.)
A spray can with volume
contains ideal gas at temperature
and pressure
(
).
b) The can is tossed into an open fire. What is
the pressure inside the can when its
temperature reaches
? (Volume and
number of particles do not change.)
A better approach:
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