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Period 8 Solutions: Internal Energy and the Laws of Thermodynamics
8.1
Internal Energy
Your instructor will discuss how changes in internal energy U relate to energy
conservation.
1) Internal Energy
Your instructor will demonstrate two rolling carts colliding with a barrier. Both carts
have the same mass and the same frictional force with the table top.
a) Which cart has more kinetic energy after it hits the barrier – the cart that rolls
back a shorter distance or a longer distance? _longer distance_ How do you
know?
The cart that rolls back a longer distance must have bounced off of the
barrier with a faster velocity. This cart has more kinetic energy
because kinetic energy is proportional to the velocity squared.
Ekin = ½ M v 2
b) Now watch the carts, without their outer covers, collide with the barrier. How can
you explain the difference in the kinetic energy of the carts after they hit the barrier?
If each cart is pushed with the same force, both carts start with the
same amount of kinetic energy. Their kinetic energy goes into moving
against the force of friction with the table top and into colliding with
the wall. Since after the collision the elastic band cart uses energy not
only to rebound, but to vibrate the washers as well, it does not roll as
far after the collision.
c) In this demonstration, what type of energy do the vibrating washers represent?
During the collision, some of the initial kinetic energy of motion of the
cart with springs is used to vibrate the washers. This kinetic energy
goes into increasing the internal energy U of the cart.
The carts demonstrate what happens inside of a solid when kinetic
energy is converted into the thermal energy of vibrating atoms and
molecules. The faster the atoms and molecules of an object vibrate,
the greater the internal energy of the object.
8.2
Work from Thermodynamic Systems
Your instructor will discuss how changes in internal energy U relate to energy
conservation and the first law of thermodynamics.
2) The Electric Drill Popper
The electric drill activity illustrates work done by an electric motor (the drill) and a
thermodynamic system (the steam in the tube). Your instructor will explain the
electric drill activity. Be sure to hold the cardboard tube over the end of the drill
while you perform this activity.
a)
How was heat Q added to the system of the drill and the stopper?
Friction between the moving drill tube and the wooden clamp produced
thermal energy.
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b)
What evidence do you have that the internal energy of this system increased?
The water in the tube became steam.
c)
How was work done by this system?
As the stopper flew up, work was done against the force of gravity and
the force of friction holding the stopper into the tube.
d)
How much work was done on the stopper by the drill if 525 joules of heat
transferred to the water resulted in a 500 joule increase in the internal energy of
the system?
W = Q – U = 525 J – 500 J = 25 J
3) Thermodynamic Systems Doing Work
a) How is work related to equilibrium?
A work or energy input is required to change a system from an
equilibrium state. As the system is moving back toward equilibrium,
the stored energy can be given off as wasted energy or can be used to
do work. For example, the electric motor runs only if there is
difference in voltage, and a steam engine runs only if there is a
difference is temperature. These devices will only run as long as a nonequilibrium situation exists.
b) Can a system ever return to a non-equilibrium state? __yes___
If so, what is necessary for the system to return to non-equilibrium?
A system can return to a non-equilibrium state only if work is done on
that system or energy is put into the system.
8.3 Reversible and Irreversible Processes
4) Reversible and Irreversible Processes
Your instructor will discuss reversible and irreversible processes.
Another version of the second law of thermodynamics, expressed in terms of
irreversible processes, is “All physical processes are irreversible.”
a) Copper and steel beads are mixed together in a beaker on your table. How can
the entropy of this mixture be decreased?
Entropy is decreased when the beads are separated into piles of copper
and piles of steel beads.
b) What must you do to decrease this entropy? What can you use to make this
process easier?
You must do work to separate the copper from the steel beads. Using a
magnet that attracts the steel beads makes this process easier.
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c) A discharging capacitor produces an electric current. This current can be used to
do work or it could be stored and then used to recharge the capacitor. Could
this current be used to recharge the capacitor to its original voltage? Why or
why not?
No. Some energy would be wasted as the charges combine to form an
electric current. The amount of energy available to recharge the
capacitor is less than the electrical energy produced by the capacitor.
d) Is the process of discharging a capacitor reversible?
No. To recharge the capacitor to its original voltage, work must be
done on the capacitor.
e) During every energy conversion, the entropy of the system increases. Use the
concepts of entropy and conservation of energy to explain why reversible
processes are not possible.
Conservation of energy tells us that energy cannot be created or
destroyed. However, in every energy conversion, the entropy of the
system increases, even if only by a small amount. Up to now, we have
described this by saying that in every energy conversion, some energy
is wasted. Therefore, the amount of energy available to reverse a
process is always less than the energy produced by the process.
5)
Perpetual Motion Devices?
Your instructor will show you examples of “perpetual motion” devices.
a)
Are any of the devices an example of perpetual motion?
No. Some run on batteries, which will eventually die, and the
others will eventually stop due to friction between the moving
parts. All of the devices will eventually stop.
b)
Is the Dippy Duck a perpetual motion device? If not, what is its source of
energy?
It is not a perpetual motion device. The dippy duck will stop
when the water evaporates from the cup. Thermal energy must
continue to heat the duck’s head in order for the water to
evaporate. Also, the dippy duck draws water from a cup that
requires someone to do work to fill the cup.
c)
Why is it not possible to build a perpetual motion machine?
The First Law of Thermodynamics (conservation of energy) says
that if you take energy out of a system, the system will slow
down. Thus, the First Law forbids a perpetual motion machine,
in which you get energy out but continue to have the energy
available to do additional work.
Perpetual motion does not exist. Since some energy is wasted in
every process, that energy must be replaced to keep a machine
working. Perpetual motion would violate the second law of
thermodynamics, which states that all physical processes are
irreversible.
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8.4
Pressure, Temperature, Volume and the Ideal Gas Law
6)
The relationship between temperature and pressure
Your instructor will illustrate the result of increasing the temperature of
molecules inside the fixed volume of a can.
a) What happens to the internal energy and the motion of the water molecules
in the can as the water is heated into steam?
As their temperature increases, the water molecules have more
internal energy. As the water molecules change phase from liquid
to steam, they move freely throughout the can with substantial
kinetic energy.
b) Pressure in the can is caused by the collisions of molecules of steam with the
can walls. When the water is heated, what happens to the speed of the
steam molecules and the pressure inside the can?
The higher the temperature of the steam, the faster the steam
molecules move, and the more frequently they collide with the walls
of the can. More collisions with the can walls results in greater
pressure inside a closed can. If the can is open, the greater
pressure causes some molecules to flow out, keeping the inside and
outside pressure the same.
c) What happens to the motion of the water molecules and the pressure inside
the closed can when the steam is quickly cooled and condenses into liquid
water?
Some of the steam molecules condense into water droplets. The
cooled water molecules no longer move freely throughout the can.
This results in fewer molecular collisions with the can walls. The
pressure inside the can decreases.
d) Why do the walls of the can collapse?
The atmospheric pressure in the room is greater than the pressure
inside the can, and the can collapses.
e) Based on your observations, is pressure P directly or indirectly (inversely)
related to temperature T?
With a fixed volume, pressure and temperature are directly related.
An increase in the temperature of a gas results in increased
pressure of the gas molecules on the walls of its container.
Pressure and temperature are directly proportional: P  T
7)
The relationship between volume and pressure
We have seen that the pressure inside the can results from steam molecules hitting
the can walls. Suppose that you change could the volume of a container of gas
without changing the temperature of the gas.
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a) If you increase the volume V of the container, but keep the temperature
constant, what happens to the number of times that gas molecules hit the can
walls? How will the pressure inside the can change?
There are more collisions with the can walls, so the pressure increases.
b) If you decrease the volume of the container, what happens to the number of
times that gas molecules hit the can walls? What happens to the pressure inside
the can?
There are fewer collisions with the can walls, so the pressure decreases.
c)
Is pressure directly or indirectly (inversely) related to volume?
At a fixed temperature, pressure and volume are indirectly related.
An increase in the volume of a gas results in decreased pressure of
the gas molecules on the walls of its container.
Pressure and volume are indirectly proportional: P 
8)
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V
The relationship between number of gas molecules and pressure
a)
If the volume and temperature of a gas are held constant and the number of gas
molecules N is increased, what happens to the number of times that the gas
molecules hit the walls of the container? How will the gas pressure change?
More molecules mean more frequent collisions with the walls of the
container. The pressure increases.
b)
Is pressure directly or indirectly (inversely) related to the number of gas
molecules?
At a fixed temperature and volume, pressure is directly related to the
number of gas molecules: P  N
9)
The Ideal Gas Law
Next we consider the relationship among pressure, temperature, volume, and
number of molecules of a gas and discuss the Ideal Gas Law.
a) You can illustrate this relationship with a pump and a liter bottle. Record the
temperature on the thermometer inside the bottle. ________________.
Pump air into the bottle. Record the temperature. _________________
Then release the pressure by loosening the pump and record the temperature
inside the bottle. __________________
Which of the four variables P, V, N, and T changed as you pumped air into the bottle?
Indicate below the change in variables.
Volume: The volume of the liter bottle is fixed.
Number of molecules: Adding more air increases the number of air
molecules.
Temperature: The thermometer indicates an increase in temperature.
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Pressure: Pressure increased as air is pumped in.
b)
c)
Write the relationship among the variables P, V, N, and T as a proportionality:
NT
P 
V
Introducing the constant k into this proportionality and rearranging the variable
V, gives the equation for the Ideal Gas Law: P V  N k T
P V  NkT
A car tire has a pressure of 30 pounds/in2 or 2.07 x 105 newtons/m2. The
o
volume of air in the tire is 0.05 meters3. The tire temperature is 27 C or 300 K.
–23
The constant k = 1.38 x 10
J/K degree. How many molecules of air does the
tire contain?
N
d)

PV
(2.07 x 10 5 N / m2 ) x (0.05 m3 )

kT
(1.38 x 10 23 J / K degree) x (300 K )

2.5 x 10 24 molecules
Group Discussion Question: The owner’s manual of a new car indicates two tire
pressures: a maximum pressure of 36 pounds/in2 and a recommended pressure
of 28 pounds/in2. To which pressure should you inflate the tires? Why?
Inflate the tires to the recommended pressure. As you drive, friction
between the tires and the road heats up the air in the tires. The heated
air will increase the tire pressure. If the tire pressure is already at the
maximum allowed, the pressure could reach a dangerous level and
affect the car’s handling and braking, or even cause a blowout.
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