PES 2130 Fall 2014, Spendier
Lecture 1/Page 1
Lecture today: Chapter 18
1) Course Introduction
2) Temperature (internal energy)
3) Heat transfer and thermal equilibrium
4) Zeroth law of thermodynamics
Thermodynamics:
- Up until now, we have looked at the physics of individual objects, whether that would
mean a “point particle” or a solid object.
- The study of thermodynamics involves a collection of objects, usually atomic in size,
and how they behave as a system.
- The development of thermodynamics drove technological developments such as the
steam engine, internal combustion engine, and fridges.
What is Thermodynamics all about?
Thermal Energy Exercise (Physics I question)
A 10-kg mass sliding to the right, initially with speed 3m/s, is stopped by friction. Where
does the mass’s kinetic energy go?
Use conservation of energy (energy cannot be created nor destroyed, the universe has a
finite amount of energy and we move it from form to form). Surface is horizontal so there
is no change in gravitational potential energy, there are no springs, so the only force that
is doing work here is friction = Wfriction
Ei  E f
1 2
1
mvi  W friction  mv 2f
2
2
1
1
2
(10kg )  3m / s   W friction  m(0m / s )2
2
2
W friction  45 J
Friction does -45 J of work on the box. What does it mean that the work done by friction
is negative? It is an opposing force that tries to slow down the block. So we have this nice
equation that tells us that friction does -45 J of work. But where does this energy go? Is it
destroyed? No! Where does it go? It goes into heat. The mass’s kinetic energy of 45 J is
absorbed by the molecules of the block, the floor, and the surrounding air.
We say that Wf = -∆Eint (minus the change of the internal energy Eint of the molecules).
PES 2130 Fall 2014, Spendier
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Chapters 18 (19 and 20) deals with the effect that this energy has on the molecules inside
each of these substances. Very roughly speaking, this is what thermodynamics is all
about. For example, we will learn that we can change the temperature of a body not just
by doing work (as our above example shows) but also by directly adding heat to it (for
example by putting a hot flame next to the object). This means that "heat" is a form of
energy!
For the upcoming chapters on thermodynamics, it is important to review a few concepts
from mechanics:
– Forces (and pressure).
– Work, energy and energy conservation.
– Potential energy.
– Momentum and momentum conservation.
Phases
All matter (objects with mass) are made out of molecules.
Molecule - collection of atoms held together by attractive forces. (Atoms are made of
smaller pieces = subatomic particles, but we won’t need them here. Thermodynamics
stops at the molecular level) What is this attractive force? It is really the electric (ionic)
force - Physics 2!
Phases (State of Matter) of Matter - Solid, liquid, or gas
In all phases of matter the molecules are moving. What distinguishes the phases of
matter? It is the amount of freedom in motion the molecules have.
The molecules’ “Degree of Freedom” determines whether the object is a solid, liquid, or
gas.
Solids: Besides being hard, what makes a solid a solid? All of the molecules have a fixed
location about which they oscillate.
Liquids: Molecules are constrained to move below the fluid surface. But within this
volume they can move anywhere they want.
Gases: Molecules can go anywhere within the container.
Besides these three phases of motion there are two, more exotic, phases of motion.
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Plasma (ionized gas): Plasma TV, sun - it is like a gas, it is gas that has become so hot
that the temperature has become so high that the electrons are now free from the nucleus.
In a plasma the electrons have gained extra freedom of motion.
We don't talk about plasmas in thermodynamics, because thermodynamics stops at the
molecule level. You cannot have water plasma. Water molecules are mode out of 2 H and
1 O. You can have a hydrogen or oxygen plasma but you cannot have a water plasma.
The sun's enormous heat rips electrons off the hydrogen and helium molecules that make
up the sun. Essentially, the sun, like most stars, is a great big ball of plasma.
Bose-Einstein Condensate (even less degrees of freedom than a solid)
There are a few atoms in this state. They are super-cooled. What happens is that these
atoms loose their freedom of identity. You cannot distinguish the atoms in a BoseEinstein Condensate. This means that is has even less freedom of motion that a solid.
In this semester we stick with solid, liquids, and gas!
In these three phases, all molecules are moving (have random speeds), and all these
molecules have kinetic energy. The molecules have a whole range of kinetic energies.
Some are going slow, some are going medium and some are going fast. As they are
colliding with each other, the molecules' speeds and directions are constantly changing.
Internal Energy, Eint: (For example friction that causes a change in internal energy)
It is the total energy (both kinetic and potential) of the molecules in a substance.
Temperature: A measure of the average (translational) kinetic energy of the
molecules
There are actually a couple of different types of kinetic energy a molecule can have.
1) Translational kinetic energy: this is the one defined by temperature
1
average value of mv 2 for water molecules is temperature
2
2) Molecules can have rotational kinetic energy. They can spin on an axis. This also a
form of internal energy.
3) Vibrational kinetic energy. What is holding molecules together is the electric force.
A very rough picture would equate the electric force with a spring force. (Taylor series
approach that shows that spring force will pop out). So a good approximation that in the a
water molecules hydrogen and oxygen are attached by a spring. Two masses on a spring
like to vibrate.
If you have a molecule rotating and vibrating it will eventually collide with other rotating
molecules. If you wait long enough rotational and vibrational kinetic energy will be
transferred into translation kinetic energy. This is why temperature is defined by the
average translational kinetic energy. This is called the Equipartition Theorem (chapter
19)
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We don't measure temperature directly. The unit of kinetic energy is joules. As we know,
we do not use this unit to measure temperature. We use other measures that are
proportional to the average kinetic energy of the molecules.
Temperature Scales
As in the case of distance, or time, we need a scale to be able to represent aspects of
nature to each other in a reproducible way.
–For distance, we take some length to be a standard (distance from here to there,
say, a meter), and then subdivide it into parts (centimeters, millimeters, etc.).
–For time, we use one revolution of the earth as a day, divide that into 24 parts
(hours), then divide each of those into 60 parts (minutes), and then divide each of
those into 60 parts (seconds).
For temperature then, we need two standard temperatures (here and there), and some way
to represent temperatures in a measureable way.
In the U.S. there are currently three temperature scales used:
The chart in the figure below shows the relationship between temperature scales, rounded
to the nearest degree.
•On the Celsius (or centigrade) temperature scale ("fake" SI unit for temperature),
0°C is the freezing point of pure water and 100°C is its boiling point at sea level. (100 is
102, based on powers of 10 = SI). It must be pure water because stuff mixed within water
will change the boiling point. For example, if you add a pinch of salt to the water it will
freeze at a temperature below zero.
The reason some foods have high altitude instruction is because the boiling point of water
changes with altitude (atmospheric pressure). As you go higher (decreasing pressure), the
boiling temperature decreases. As a general rule, the boiling point temperature decreases
by 0.56° C for every 165 meters. On top of the14,000 foot Pike's Peak, for example, the
boiling point of water is 187° F (86° C).
•On the Fahrenheit temperature scale, 32°F is the freezing point of pure water and
212°F is its boiling point at sea level.
•On the Kelvin (or absolute) temperature scale ("real" SI unit for temperature), 0 K
is the extrapolated temperature at which a gas would exert no pressure. (real physical
scale)
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The Kelvin scale is based on the physical definition of temperature.
Lower temperature ==> lower kinetic energy ==> slower speeds (speed has no negative
value)
Absolute Zero (0 K) - The lowest possible temperature. At absolute zero, all molecular
motion would stop.
Third law of Thermodynamics (discovered in the early 19 hundreds): It is impossible to
reach absolute zero, no matter what physical process you may use to make the molecules
absolutely stop. The phenomenon called quantum mechanics won't allow this to happen.
So people have been trying to see how close they can get to the impossible. At the
moment the record is ~1 pK
Temperature Conversions
The spacing on the Kelvin scale was chosen to be the same as the Celsius scale
T ( K )  T ( C ) . So any equation with ∆T can use either Kelvin or Celsius. From
experiment, 0K = -273°C, hence
T  TC  273 C
T  Kelvin temperature
TC  Celsius temperature
The relation between the Celsius and Fahrenheit scales is
9
TF  TC  32 C
3
TF  Fahrenheit temperature
Thermal Equilibrium
When two objects of different temperatures are placed in thermal contact, thermal energy
(wiggling and colliding molecules) will be transferred from the object with the higher
temperature to the object with the lower temperature.
(a) Two bodies A and B are of different temperatures, the temperature of A is higher than
that of B.
(b) When they are in contact, heat is transferred from A to B. The side of B touching A
will "heat" up first causing a temperature gradient.
(c) The net energy (heat) transfer will stop when both A and B reach the final temperature
==> A and B reached Thermal Equilibrium.
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Why is this so obvious? The higher temperature object has more kinetic energy than the
lower temperature object, so if the higher temperature object got extra energy and cannot
destroy it, the energy has to be given spontaneously to the object which has less energy.
So this energy transfer from hot to cold is just a conservation of energy statement. As the
heated particles collide with their colder neighbors, energy is transferred from the hot
side to the cold side of the object (known as conduction).
Note that in reality it is difficult to isolate A and B from their surrounding and some of
the thermal energy will be transferred to and from air molecules. For example, the
temperature in a room, or the temperature which surrounds an object under discussion, is
called ambient temperature.
Zeroth law of thermodynamics:
If C is initially in thermal equilibrium with both A and B, then A and B are in
thermal equilibrium with each other.
As we will talk about in more detail later, there are ways to make heat flow nonspontaneously. The air-conditioning in the room is doing so. The air-conditioned room is
colder than its surroundings. It is staying cooler because the air conditioner is removing
heat.
Heat Q:
The transferred energy is called heat and is symbolized Q. Heat spontaneously flows
from higher to lower temperature.
Heat is positive when heat is absorbed by the system.
Heat is negative when heat is released or lost by the system.
Relevant concept to solve problems:
When heat flow occurs between two or more objects that are isolated from their
surroundings, the algebraic sum of the quantities of heat transferred to all bodies is zero:
∑
Before scientists realized that heat is transferred energy, heat was measured in terms of
its ability to raise the temperature of water.
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The calorie (cal) was defined as the amount of heat that would raise the temperature
of 1 g of water from 14.5°C to 15.5°C.
The British thermal unit (Btu), defined as the amount of heat that would raise the
temperature of 1 lb of water from 63°F to 64°F.
Then the scientific community decided that since heat (like work) is transferred energy,
the SI unit for heat should be the one we use for energy— namely, the joule.
1 cal = 3.968 x 10-3 Btu = 4.1868 J.
Heat’s Effects:
DEMOS: Heat effects
- Thermal expansion
1) ball in hole
2) bimetal (black side up)
- Phase change (change of state)
1) hand boiler: When one bulb is held in your hand body heat causes the volatile
liquid inside to boil (volatile liquid = Liquid that evaporates at room temperature)
Heat can have three different effects on objects:
1) Thermal Expansion.
2) Change in temperature.
3) Change in phase.
1) Thermal Expansion: Change in length (volume) due to temperature changes.
Thermal expansion of materials with an increase in temperature must be anticipated in
many common situations Applications:
- Loosen a tight metal jar lid by holding it under a stream of hot water. The atoms
in the metal move farther apart than those in the glass. Hence, the lid expands
more than the jar and thus is loosened.
- When a bridge is subject to large seasonal changes in temperature, for example,
sections of the bridge are separated by expansion slots so that the sections have
room to expand on hot days without the bridge buckling.
Let us try to understand what happens to a substance when heated by modeling the atoms
as being held together by springs.
a) We can model atoms in a solid as being held together by "springs" that are easier to
stretch than to compress.
b) A graph of the "spring" potential energy U(x) versus distance x between neighboring
atoms is not symmetrical. As the energy increases the atoms oscillate with greater
amplitude and the average distance increases.
PES 2130 Fall 2014, Spendier
Therefore, increasing the temperature of a rod causes it to expand.
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