The Laws of Thermodynamics
Dynamics is the study of why things move the way they
do. For instance, in the chapter on dynamics, we looked at Newton’s
Laws to explain what compels bodies to accelerate, and how. The
prefix thermo denotes heat, so thermodynamics is
the study of what compels heat to move in the way that it does.
The Laws of Thermodynamics give us the whats and whys of heat flow.
The laws of thermodynamics are a bit strange. There are
four of them, but they are ordered zero to three, and not one to
four. They weren’t discovered in the order in which they’re numbered,
and some—particularly the Second Law—have many different formulations,
which seem to have nothing to do with one another.
There will almost certainly be a question on the Second
Law on SAT II Physics, and quite possibly something on the First
Law. The Zeroth Law and Third Law are
unlikely to come up, but we include them here for the sake of completion.
Questions on the Laws of Thermodynamics will probably be qualitative:
as long as you understand what these laws mean, you probably won’t
have to do any calculating.
If system A is at thermal
equilibrium with system B, and B is
at thermal equilibrium with system C,
then A is at thermal equilibrium with C.
This is more a matter of logic than of physics. Two systems are
at thermal equilibrium if they have the same temperature. If A and B have
the same temperature, and B and C have
the same temperature, then A and C have
the same temperature.
The significant consequence of the Zeroth Law is that,
when a hotter object and a colder object are placed in contact with
one another, heat will flow from the hotter object to the colder
object until they are in thermal equilibrium.
Consider an isolated system—that is, one where heat and
energy neither enter nor leave the system. Such a system is doing
no work, but we associate with it a certain internal energy, U,
which is related to the kinetic energy of the molecules in the system,
and therefore to the system’s temperature. Internal energy is similar
to potential energy in that it is a property of a system that is
doing no work, but has the potential to do work.
The First Law tells us that the internal energy of a system
increases if heat is added to the system or if work is done on the
system and decreases if the system gives off heat or does work.
We can express this law as an equation:
where U signifies internal
energy, Q signifies heat, and W signifies
The First Law is just another way of stating the law of
conservation of energy. Both heat and work are forms of energy,
so any heat or work that goes into or out of a system must affect
the internal energy of that system.
heat is added to a gas container that is topped by a movable piston.
The piston is weighed down with a 2 kg mass. The piston rises a
distance of 0.2 m at a constant velocity. Throughout this process,
the temperature of the gas in the container remains constant. How
much heat was added to the container?
The key to answering this question is to note that the
temperature of the container remains constant. That means that the
internal energy of the system remains constant (
), which means that, according to the First
. By pushing the piston upward, the system
does a certain amount of work,
, and this work must be
equal to the amount of heat added to the system,
The amount of work done by the system on the piston is
the product of the force exerted on the piston and the distance
the piston is moved. Since the piston moves at a constant velocity,
we know that the net force acting on the piston is zero, and so
the force the expanding gas exerts to push the piston upward must
be equal and opposite to the force of gravity pushing the piston
downward. If the piston is weighed down by a two-kilogram mass,
we know that the force of gravity is:
Since the gas exerts a force that is equal and opposite
to the force of gravity, we know that it exerts a force of 19.6 N
upward. The piston travels a distance of 0.2 m, so
the total work done on the piston is:
in the equation for the
First Law of Thermodynamics is positive when work is done on the
system and negative when work is done by the system, the value of
is –3.92 J
, we can conclude that J
, so 3.92 J
heat must have been added to the system to make the piston rise
as it did.
There are a number of equivalent forms of the Second Law,
each of which sounds quite different from the others. Questions
about the Second Law on SAT II Physics will invariably be qualitative.
They will usually ask that you identify a certain formulation of
the Second Law as an expression of the Second Law.
The Second Law in Terms of Heat Flow
Perhaps the most intuitive formulation of the
Second Law is that heat flows spontaneously from a hotter object
to a colder one, but not in the opposite direction. If you leave
a hot dinner on a table at room temperature, it will slowly cool
down, and if you leave a bowl of ice cream on a table at room temperature,
it will warm up and melt. You may have noticed that hot dinners do
not spontaneously get hotter and ice cream does not spontaneously
get colder when we leave them out.
The Second Law in Terms of Heat Engines
One consequence of this law, which we will explore a bit
more in the section on heat engines, is that no machine
can work at 100% efficiency: all machines generate some heat, and
some of that heat is always lost to the machine’s surroundings.
The Second Law in Terms of Entropy
The Second Law is most famous for its formulation in terms
of entropy. The word entropy was coined
in the 19th century as a technical term for talking about disorder.
The same principle that tells us that heat spontaneously flows from
hot to cold but not in the opposite direction also tells us that,
in general, ordered systems are liable to fall into disorder, but
disordered systems are not liable to order themselves spontaneously.
Imagine pouring a tablespoon of salt and then a tablespoon
of pepper into a jar. At first, there will be two separate heaps:
one of salt and one of pepper. But if you shake up the mixture,
the grains of salt and pepper will mix together. No amount of shaking
will then help you separate the mixture of grains back into two
distinct heaps. The two separate heaps of salt and pepper constitute
a more ordered system than the mixture of the two.
Next, suppose you drop the jar on the floor. The glass
will break and the grains of salt and pepper will scatter across
the floor. You can wait patiently, but you’ll find that, while the
glass could shatter and the grains could scatter, no action as simple
as dropping a jar will get the glass to fuse back together again
or the salt and pepper to gather themselves up. Your system of salt
and pepper in the jar is more ordered than the system of shattered
glass and scattered condiments.
Entropy and Time
You may have noticed that Newton’s Laws and the laws of
kinematics are time-invariant. That is, if you were to play a videotape
of kinematic motion in reverse, it would still obey the laws of
kinematics. Videotape a ball flying up in the air and watch it drop.
Then play the tape backward: it goes up in the air and drops in
just the same way.
By contrast, you’ll notice that the Second Law is not
time-invariant: it tells us that, over time, the universe tends
toward greater disorder. Physicists suggest that the Second Law
is what gives time a direction. If all we had were Newton’s Laws,
then there would be no difference between time going forward and
time going backward. So we were a bit inaccurate when we said that
entropy increases over time. We would be more accurate to say that
time moves in the direction of entropy increase.
It is impossible to cool a substance to absolute zero.
This law is irrelevant as far as SAT II Physics is concerned, but
we have included it for the sake of completeness.