Introduction to the Zeroth and First Laws of Thermodynamics

While studying some material from chem. 203 (physical chemistry for life science majors), I have come up with these notes. I hope they will be helpful to other people in a course such as this one, since the textbook, the lecture material, and additional online notes should be more condensed. But, use at your own risk. I may include some of the problem sets that I have solved, but it is truly a pain to type them out using the primitive equation writing programs on my computer.

The Zeroth Law of Thermodynamics:

Given a body A and a body B in thermal equilibrium, then a body C in thermal equilibrium with body B, is also in thermal equilibrium with body A.

In other words:

If A = B

And B = C

Then A = C

Of course, what does thermal equilibrium mean?

Heat flows from hot to cold bodies. Thermal equilibrium is the point where the two bodies acquire the same temperature.

The First Law of Thermodynamics:

U = q + w

Where U = the internal energy of a system

q = the heat flow into the system

w = the work done on the system

This law tends to be a bit confusing because it involves a concept that it is more abstract called the internal energy, denoted U. To measure U in absolute form would be impossible, but to measure  is much more manageable. (As in, you’ll be asked to calculate it!) It is proportional to the temperature of the system, and has to do with molecular movement, including the kinetic and potential energy of the motion of individual molecules, attractions between molecules, and the nuclei and electrons within the individual molecules.

Just as an aside, if you think about all of these properties being additive, the absolute internal energy of a system seems to be infinite (I don’t know if this is actually right or not), because you are moving into smaller and smaller scales of motion. This shows it to be impractical to calculate this state function of a system. However, a change in the internal energy would be on a much smaller scale, so it would be worth calculating for comparison purposes and such.

The heat component of this equation is pretty straight forward. If heat enters the system, it will be a positive value. If heat leaves the system, it will be a negative value, as the system is experiencing a loss.

Work, on the other hand, is a little less intuitive. Work done on the system is positive, whereas work done by the system is negative. This is a convention and must be memorized.

But – wait a second? What is an example of work done by and work done on? The easiest way to think about it, is from the favourite diagram in your text book of a cylinder of gas with a piston bearing a weight. If the gas expands, then work is done by the system. If the gas compresses, then work is done on the system.

I will dedicate an entire post to work in the First Law of Thermodynamics, since the concept is important, and I’d like to spend more time on it – so stay tuned.

Now, back to the First Law.

Another concept that is a fond testing subject of numerous multiple choice style exams, is that of state functions. Most explanations are a bit ambiguous as to what this actually means.

The first thing to wrap our heads around is the part about states.  Thermodynamics is concerned with equilibrium states. Most of the changes of state in pure thermodynamics occur at infinitesimal rates to ensure no exchanges happen with the environment and no sudden changes occur in certain properties. (For example, the cylinder of gas with that piston and mass. The piston would move up very slowly to keep the forces in balance at equilibrium.) However, this is an ideal situation, and in reality the changes would probably occur in nonequilibrium conditions. Thermodynamics doesn’t care about that though. Processes that occur at equilibrium are said to be reversible.

So, state functions are properties that describe the state of the system, such as mass, pressure, temperature and volume. But what makes them so? If you consider a change in a state function, the change is independent of the path taken to achieve the change. This can be illustrated by examining the walk between your apartment and St. Viateur bagel shop. There are many routes to get there, but the shortest distance is to travel in a straight line from the apartment to St. Viateur. You many take many other longer routes, but the end result is the same, you eat your sesame seed bagel warm from the oven. In fact, the other methods waste energy to achieve the same result!

Applying this to the First Law, the internal energy is a state function. BUT! Work and heat are not, as they are path dependent functions.