Physics 111
Solutions to Essay Questions 4
1.
The cylinder of gas shown has a piston that can float up and down.
You can:
Lock or unlock the piston
Add or remove masses from the piston
Place the entire cylinder in a hot or cold liquid
a.
Locking pin
Can you increase the gas temperature without changing the pressure? If so, describe
how you would do it. If not, explain why not.
Yes, you can increase the gas temperature without changing the pressure. The pressure inside the
cylinder is determined by the outside atmospheric pressure (which we will assume to be fixed) and
by the weight of the masses and piston divided by the area of the piston. So, as long as we do not
change the mass on the piston, the pressure will be constant. Therefore, we should immerse the
cylinder in a hot liquid. This means the volume will increase, the thermal energy will increase, work
will be done by the gas on the environment. Make sure the locking pin in not inserted!
b.
Can you increase the gas pressure without changing the temperature? If so, describe
how you would do it. If not, explain why not.
From the previous part, we know we can increase the pressure by adding masses. If we add the
masses too quickly, the gas will compress adiabatically and the temperature will increase. So we
need to add the mass gradually while the cylinder is immersed in a cooler liquid. Then, the energy
added by the piston doing work on the gas will be transferred to the environment as heat instead of
increasing the system’s thermal energy. Again, make sure the locking pin in not inserted.
2.
A piece of cork floats in a pail of water that rests on the floor of an elevator.
a.
b.
c.
d.
a.
Draw a free body diagram of the cork when the elevator is at rest.
If the elevator moves upward at a constant velocity, how does the depth at which the
cork floats change? Why? If it does not change, why not?
If the elevator accelerates downward, how does the depth at which the cork floats
change? Why? If it does not change, why not?
You are carrying a helium-filled balloon in your car. When you accelerate forward,
which direction does the balloon move relative to the car?
Buoyant force FB
Weight mg
b.
If the elevator is moving up at constant velocity, the depth at which the cork floats will not be
different from the depth when the elevator is at rest. In both cases, the cork is in equilibrium, so the
net force is zero. Therefore, the buoyant force is equal to the weight in both cases and the same
amount of the cork must be submerged to displace a volume of water that has the same weight as the
cork.
c.
If the elevator is accelerating down, the weight must be greater than the buoyant force
supporting it. Since the weight of the cork does not change, it must rise compared to the water level,
displacing less water and decreasing the buoyant force.
d.
If you accelerate forward, the inertia of the air resists acceleration and the air shifts so that it
is denser in the back of the car and less dense in the front. The helium balloon will feel more
pressure on its backside than it front side, so it will accelerate forward. Other explanations are
possible, such as the idea that accelerating forward acts effectively like giving the acceleration of
gravity a backwards horizontal component.
3.
One whimsical statement of the laws of thermodynamics is, “You can’t win, you can’t break
even, and you can’t get out of the game.” Justify this statement in a clearly written paragraph.
A good answer will mention the following facts.
“You can’t win” means that the first law of thermodynamics forbids processes that create energy.
Energy conservation implies that only transformations of energy are possible.
“You can’t break even” means that the second law of thermodynamics implies that you can
never get out as much energy from a system as the energy you put in. No engine is 100%
efficient; no refrigerator has an infinite coefficient of performance. There are no perpetual
motion machines, free refrigerators, etc.
“You can’t get out of the game” is another consequence of the second law. The entropy of the
universe (or any isolated subsystem) never decreases. Energy in macroscopic systems is
continually and irreversibly being converted from more useful forms of energy to less useful
forms of energy. The consequence of this is sometimes called “the heat death of the universe”:
as time goes on, the universe will come closer and closer to equilibrium until there are not
temperature differences left to drive heat engines (such as living organisms).