of freedom; both the pressure and the temperature are fixed. Any attempt
to change either P or T would necessarily cause a disappearance of one of
the phases, and we would move along the line of equilibrium between two
phases.”
“That is awesome,” thought Alice. The idea of one and two degrees of
freedom had hardly sunk in and now the professor was talking about ‘zero
degrees of freedom.’ She wondered how the water molecules ‘felt’ having no
freedom. Did it mean that they cannot move at all? Were they confined, like
prisoners locked up in a solitary cell?
Alice was starting to get impatient again. She had hardly processed what
the professor had been explaining, and then came more and more complicated
ideas. Much as she wanted to focus, her mind began to drift away from
the discussion. She imagined herself in the microscopic world. ‘Phases’ and
‘degrees of freedom’ — how significant were they to water molecules? Did
water molecules ‘know’ or ‘feel’ when they had one or two degrees of freedom?
It all overwhelmed Alice.
She did not understand why the three lines converge at a single point. She
remembered from geometry that every two straight lines meet at one point,
and if the lines are curved, then the two lines can cross at more than one point.
But here the professor had explained that three curved lines meet at a single,
unique point — and no more.
After rehearsing the question in her mind a few times, she raised her hand
nervously.
“Professor, how come the three curves intersect at only one point?” she
asked.
“That is a very good question,” replied the professor. “The answer to your
question is not trivial. You are right that two curved lines can intersect at any
number of points, and three lines—even straight lines—can intersect at zero,
one, two or three points. But that is true if you select the lines at will.
“Here we have a different situation. The form of the curves is determined
by the properties of the system; they are not chosen at will. It is an experimental