Geysers are among the
most popular attractions at Yellowstone National Park. A geyser is a vertical
hole in the ground that gradually fills with water and leads down to a source
of volcanic heat. After a dormant period of minutes or hours, water comes
rushing up out of the hole and sprays vigorously into the sky. A geyser is a
spectacular heat engine and it functions in part through the use of water's
material phases.
1. After it erupts, the geyser's hole refills with water so that the water forms a tall, narrow, vertical column in a solid rock "pipe." The rocks at the bottom of this pipe are volcanically heated and heat flows from those rocks into the water. The temperature of water at the base of the pipe soon exceeds 100 °C, yet the water doesn't boil. Explain why the water doesn't boil.
Answer: The water pressure at the base is extremely
high and the boiling temperature of water increases with the pressure.
Why: The weight of all
the water overhead in the pipe produces an extremely high pressure near the
base of the pipe. The boiling point of water near the base is therefore
increased dramatically. That's because the vapor pressure of steam in any
bubble that forms must exceed the ambient pressure for that bubble to grow. At
this enormous pressure, the bubbles don’t begin to grow until the water
temperature rises far above 100 °C.
2. Eventually water at the base of the pipe does begin to boil. When this occurs, the steam bubbles push a little of the water out of the pipe's top, where it trickles down around the opening of the geyser. After a few seconds of this trickling, the geyser erupts violently, spraying water high into the air. Why did losing just a little bit of water from the top of the pipe cause this sudden and dramatic eruption?
Answer: The lost water reduces the pressure
throughout the pipe, reducing the boiling temperature of the water so that it
can boil easily.
Why: With the weight
overhead reduced, the pressure in the pipe drops and boiling can occur at a
lower pressure. The drop in boiling temperature leads to vigorous boiling,
which in turn leads to more loss of water overhead. The whole process gets
carried away: the pressure plummets as the boiling skyrockets.
3. The geyser is certainly a heat engine--it uses the flow of heat from hot rocks to cold air to do the work of tossing water high into the air. Evidently, some thermal energy from the rocks is being converted into work. Explain the process in which that thermal energy is converted to work, showing both that work is done on the water and that thermal energy is used up while doing that work.
Answer: The steam bubbles at the bottom of the pipe
push the water upward and it moves upward, so the steam does work on the water.
The steam has expanded by doing work on its surroundings, therefore it has used
some of its thermal energy (the only energy it has to work with so long as it
stays a gas) to do work.
Why: The steam pushes up
on the water and the water moves up, so the steam has clearly done work on the
water. Energy has been transferred from the steam to the water. The steam
expands during this process and expanding gases cool as long as they remain
gases and no further heat flows into them. Microscopically, the steam molecules
are bouncing off an outward-moving surface, so they rebound with less kinetic
energy than they had when they hit that outward moving surface. They slow down
and the steam cools.
4. When a geyser has finished spraying out water, it releases a great deal of an invisible gas that quickly turns into white clouds once it enters the air. What is that invisible gas?
Answer: Steam.
Why: We often think of
steam as a cloudy, white "gas," but that white mist is actually just
tiny liquid droplets suspended in the air by drag forces. Instead, steam is a
truly invisible gas. After all, about 4% of the molecules in ordinary air are
actually water molecules, and we see right through them.
Most ski resorts have
snowmaking equipment to carry them through periods of low precipitation. While
there are a number of ways to produce snow particles out of water, the most
common scheme involves mixing water and compressed air as they spray out
through nozzles into the cold night air. The compressed air helps to break up
the water into tiny droplets and project those droplets high into the air, but
it has other effects as well.
5. To make the compressed air, a ski resort squeezes ordinary outdoor air to approximately 8 times its normal density. How does this process affect the air's pressure and temperature?
Answer: The air's pressure and temperature both
increase.
Why: Compressing gases
always involves doing work on those gases. As long as no heat is exchanged with
the outside world, the gas's thermal energy will increase, and with that energy
increase come increases in temperature and pressure.
6. The compressed air then passes through a heat exchanger that allows it to reach thermal equilibrium with the outdoor air. In the process, a great deal of liquid water condenses out of the compressed air and is removed so that it doesn't ice up the pipes as the compressed air travels up the mountains. Why does water condense out of the compressed air as that compressed air passes through the heat exchanger?
Answer: Compressing the air shifts the equilibrium
balance between steam and liquid water. With the vapor-phase water molecules
packed so tightly, they return to the liquid phase more often than they leave
the liquid phase, so the liquid phase grows at the expense of the vapor phase.
Why: Before it was
compressed, moisture in the air was roughly in equilibrium with moisture on the
ground. More specifically, we are pretty sure that water molecules weren't
returning from the air's vapor phase to the ground's solid or liquid water
phases more rapidly than they were leaving for the vapor phase. But once the
air has been compressed and cooled back to normal temperatures, the moisture in
the vapor phase is tightly packed and the balance between the gaseous and
non-gaseous phases is upset. More gaseous phase molecules return to the liquid
or solid phases than leave those phases, so the vapor phase molecules condense
or frost.
7. In the snowmaking machine itself, a nozzle sprays a jet of liquid water into the outdoor air. The water enters the nozzle at about 0 °C--its freezing temperature. Although the outdoor air is slightly below 0 °C, it takes a while for the water to freeze into ice. Why doesn't 0 °C water turn into ice immediately when exposed to air that's colder than 0 °C?
Answer: Heat must be removed from 0 °C water to
convert it into 0 °C ice.
Why: There is a latent
heat in liquid water that must be released and removed before that liquid can
become solid ice. The latent heat is essentially a chemical potential energy
associated with the tighter bonding of the water molecules in ice than in
liquid water.
8. To speed the freezing process, the jet from the water nozzle mixes with the jet from a compressed air nozzle. Air spraying out of this second nozzle not only breaks up the water into tiny droplets, but it helps to cool and freeze those droplets as well. However, the compressed air and the water both enter their nozzles at the same temperature--about 0 °C. Explain how this expanding jet of compressed air is able to help chill the water jet.
Answer: The expanding air does work on the
surrounding air and its temperature decreases as a result. Heat flows out of
the water jet into this expanding jet of air and the water freezes into ice.
Why: The compressed air
enters the nozzle at ambient temperature but as it expands into the open air,
this high-density air cools dramatically. It is doing work on the open air,
pushing that open air out of its way to make room for itself as it expands to
normal density and pressure. Doing this work takes away a good fraction of the
compressed air's thermal energy, so it becomes quite cold. Heat flows into it
from the water droplets and those water droplets freeze into artificial snow.