The melodious chime of the cuckoo clock roused Alice from her sleep. Looking
around her room, which was bathed in the morning sun, she exclaimed, “What
a beautiful day!”
Alice was still overwhelmed by the experience of the previous day. It seemed
she now knew some secrets no one else was aware of — except, of course, the
professor, the inventor of the shrinking machine.
She was eager to learn more and to experience first hand what the professor
meant by the two degrees of freedom. She understood that the phase map
was merely a metaphor for the real phase diagram. She also understood what
it meant to increase or decrease the pressure and the temperature. In fact, not
only had she understood, but she had actually experienced it with her senses.
But how were these concepts of pressure and temperature seen, or perceived,
in the microscopic world?
Alice was unusually quiet at breakfast, and it had not escaped her mother’s
attention. The girl seemed to be lost in thought over some unknown problem.
“What’s bothering you, sweetie? You look as if you’re carrying the weight
of the world on your shoulders,” said Alice’s mother, finishing her sentence
with a chuckle.
“Oh Mom, don’t be silly. I was just thinking about our lesson the other day.
The professor explained things so clearly that I can’t think about anything else.
Science classes are rarely so interesting and exciting!”
45
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46 Alice’s Adventures inWater-Land
Fig. 4.1 The gadget.
She did not tell her mother
about the shrinking machine as she
wasn’t sure how her mother would
react. Besides, she had no idea how
it worked so she was in no position
to explain anything—especially to
her mother.
“I’d better get going, Mom. Professor
Holmes promised to help me
out with some experiments.” Alice
picked up her plate and mug and
put them in the dishwasher.
On the way to the laboratory, Alice rehearsed her questions for the professor.
Learning something new each day was fueling her enthusiasm to find out
more. As she entered the foyer, the mysterious girl in the portrait welcomed
her again. But before she could ask a single question she had written down her
on her notepad, the professor appeared and handed her a gadget. The device
had two knobs marked with the letters T and P (Fig. 4.1).
According to the professor, with these two knobs Alice would be able to
navigate through the TP map. Turning the T knob to the right was equivalent
to increasing the temperature while turning the P knob to the right increased
the pressure.
“These two dials will allow you to manipulate the two degrees of freedom,”
explained the professor. “In the real macroscopic laboratory we can take a
sample of gas — water or any other substance — and we can control the
pressure on a piston by adding different weights (Fig. 4.2), or the temperature
by heating the system (Fig. 4.3). As you can very well remember, each point
on the phase map corresponds to a point in the TP diagram — one specific
temperature, T, and one specific pressure, P. Let me explain the correspondence
between the macroscopic experiment we carry out in the laboratory and the
virtual motion in the phase diagram.”
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The Second Visit to theWater Vapor 47
1kg
3kg
2kg
4kg
P=1 P=2
P=3 P=4
Fig. 4.2 Effect of pressure on the volume of a gas.
T T=4
T=1
T=2 T=3
Fig. 4.3 Effect of Temperature on the volume of the gas.
The professor showed her a cylinder sealed with a piston. On the piston
were a few weights, and under the cylinder, a burner.
“By adding or removing weights on the piston,” the professor went on,
“we can increase or decrease the pressure in the gas contained in the cylinder.
This corresponds to the virtual motion, up or down (or north or south) in
the phase map. On the other hand, we can either heat or cool the gas —
i.e., the temperature will increase or decrease. This corresponds to the virtual
motion east or west in the phase map. All these correspond to macroscopic
experiments. Your task today will be to experience the microscopic view of
these experiments.”
Alice was very clear about the macroscopic experiment, but she could not
imagine what the corresponding microscopic experiment would look like—or
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48 Alice’s Adventures inWater-Land
feel like. She wondered how she would feel the high pressures when she turned
the P knob, and whether she would feel cold or warm when she turned the
T knob. Would turning either one to the extreme left or extreme right make
her feel very cold or very warm? She found the idea quite frightening.
The professor seemed to have read Alice’s mind. Even before she could
utter a word, he started to explain that what she experienced in the microscopic
world would be very different from how she experienced pressure and
temperature in real life. In the macroscopic world, you feel the temperature
and the pressure through your skin, since there are nerve cells under the skin
that respond to changes in pressure or temperature. These send messages to
the brain, where they are processed to produce either the sense of pressure or
temperature. You can also measure the temperature and the pressure using the
appropriate instruments — the thermometer and the barometer.
“Human beings have experienced the macroscopic world since time
immemorial. They have sensed the temperature and the pressure of the air.
But experiencing temperature and pressure is one thing; understanding them
is quite another. What you are going to explore today is quite different from
the macroscopic experience you encounter in the laboratory. The microscopic
view of vapor is based on an understanding of the pressure and temperature
of the gas at a molecular level.”
“To experience the microscopic view, you have to use the shrinking
machine, observe and take notes of what you see. However, to be able to
absorb and fully grasp what you experience, you will need some additional
‘brain power!’ I say this not because I have doubts about your intelligence, but
because I know that for almost 2000 years these phenomena were not well
understood at a microscopic level. Even after two giants of physicists, James
Clerk Maxwell and Ludwig Boltzmann, explained these phenomena it was not
easy to convince even their fellow scientists of the late 19th century.”
“Would you like to experience the microscopic view first and leave the
understanding for later? Perhaps, it would be a good idea if you observe first
and then we can discuss it later. That way you will not be overwhelmed. You
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The Second Visit to theWater Vapor 49
should know, however, that no
scientist has ever experienced the
microscopic view. My machine
is only a simulated experiment
based on what scientists have
learned,” the professor added.
Alice decided to forgo the use
of the IQ machine. She could
always use it some other time.
Alice was very eager to experience
the microscopic world—so
eager, in fact, that she was getting
quite impatient. She was confident
that her brain—without being ‘charged’—would be able to absorb and
process everything. Gone was her feeling of creepiness as she stepped inside
the shrinking machine. She knew what to expect this time and no longer found
the machine daunting.
All of a sudden, she was back in the microscopic world. Everything was
exactly the same as in the previous day’s encounter — water molecules were
flying in straight lines, vibrating rotating, rotating and occasionally colliding
with one another—but today’s scene seemed so real to Alice. A day earlier, the
molecules were like images painted on canvas, but this time those very same
images seemed to have come to life, vibrant and pulsating.
“This is getting so exciting,” said Alice to herself. “I am really getting to
love this!”
She felt as if she could actually reach out to those images, feel and touch
them. Deeply absorbed by what she had witnessed, she almost forgot why she
was there in the first place until she remembered the TP gadget. She decided to
use it and find out for herself how it worked.
Alice started with the P knob, turning it slowly counterclockwise to a lower
setting, which meant lower pressure. As she turned the dial, there was no
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50 Alice’s Adventures inWater-Land
discernible change at first although she noticed that there seemed to be fewer
water molecules and the collisions between the water molecules had become
increasingly infrequent. She turned the dial all the way down to almost zero.
Most of the water molecules disappeared. It was almost total emptiness —
a vacuum! Only once in a while would a molecule cross the chamber where
Alice sat.
When Alice finally reached zero on the P dial, all the water molecules had
vanished, and she felt completely alone. Was this the way it felt at low pressures?
She would ask the professor about it, or perhaps she would tell him how
it feels. She wondered where all the molecules had gone.
Alice then turned the P knob clockwise and the water molecules started to
appear. As she continued to turn the dial towards higher pressures, she noticed
that more and more water molecules appeared, and the collisions occurred
more frequently. At times, two molecules collided, and sometimes even three
or more molecules. She did not feel any pressure change although the scale
showed first 2 atm, then 3 atm, and before long, 10 atm.