## Saturday, February 18, 2012

### The Laws of Thermodynamics

If one looks around the Internet, he or she can find a multitude of pages that state the laws of thermodynamics; so why add one more?  I've been writing a lot of posts on thermodynamics, but nowhere have I given a concise statement of the laws; also, I am not always happy with how the laws are described.  So this post is my contribution.

The Zeroth Law of Thermodynamics

The zeroth law states:
If two bodies are in thermal equilibrium with a third body, then they are in thermal equilibrium with each other.

For those who have studied mathematics, this law may seem obvious.  Perhaps, it should not seem so obvious when one considers all the ways that macroscopic bodies can store energy. At some point I may write a post devoted to this law.  Note that this law is essential to defining such a thing as temperature. Two bodies at the same temperature are in thermal equilibrium with each other.

Two bodies are in thermal equilibrium if they have reached the final temperature that they will reach if allowed to exchange heat with one another. At such a point, no net heat is exchanged.  In many ways, the zeroth law depends on an understanding of the other laws. One could use the mnemonic, "let's keep score" for the zeroth law, but that phrase is usually used for the third law.

The First Law of Thermodynamics

I have written a post that goes into more depth on the first law of thermodynamics. The first law states:
Heat is not a conserved quantity, and work is not a conserved quantity, but the sum of heat and work is a conserved quantity.
The sum of heat and work is called the internal energy. Conservation of internal energy is a special case of the more general principle of conservation of energy.  Conservation of energy can be derived from Noether's Theorem, which is perhaps one of the most profound theorems of physics.

The internal energy is a state function.  Its value does not depend on the path taken.  Another example of a state function that is closely related to the internal energy is a quantity called enthalpy. A mnemonic for remembering the first law is "you cannot win."  You cannot get more energy out of a system than you put in.

The Second Law of Thermodynamics

I have written a series of posts on the second law of thermodynamics. It is my contention that this law is one of the most misunderstood and abused law in the sciences. There are several different ways to state the second law; here I'll stick to one:
There can be no process with the sole result of absorbing heat and completely converting it to work.
A mnemonic for remembering this law is "you cannot break even."

The second law is intimately connected to a state function called entropy.  Entropy is often falsely stated to be a measure of disorder. Whereas the entropy is a mathematical relationship between the heat transferred reversibly, and the thermodynamic temperature, it can also be described from a statistical-mechanical viewpoint as a quantity related to the number of  ways to arrange a system with a given energy range.

The Third Law of Thermodynamics

I have written a post on the third law of thermodynamics.  It states:
It is impossible to reach absolute zero in a finite number of steps.
A mnemonic for this law is "you cannot leave the game."  Alternatively, a mnemonic is "let's keep score."  This one arises because the third law is the basis for the thermodynamic temperature scale.  It is possible, however, to define a temperature scale based upon the zeroth law.  The third law is greedy: it gets two mnemonics, whereas the zeroth law gets zero.  In the spirit of fair play, I assign one  of the third law's mnemonics to the zeroth law.

Mnemonics
• 0th Law: "Let's keep score."
• 1st Law: "You cannot win."
• 2nd Law:  "You cannot break even."
• 3rd Law: "You cannot leave the game."
Sources

• Atkins, P. W. Physical Chemistry, W. H. Freeman and Company, New York, 3rd edition, 1986
• McQuarrie, Donal d A., Statistical Thermodynamics,  University Science Books, Mill Valley, CA, 1973
• Bromberg, J. Philip, Physical Chemistry, Allan and Bacon, Inc., Boston, 2nd Edition, 1984
• Feynman, Richard P., Leighton Robert B., Sands, Matthew, The Feynman Lectures on Physics, Addison-Wesley, Menlo park, CA, 1965

Bryan said...

Let's keep score + You cannot win + You cannot break even + You cannot leave the game

No wonder Boltzmann killed himself!

Rich said...

Thanks for the comment. Perhaps, thermodynamics should have been called the dismal science!

James Thompson said...

Hardly dismal. The undeceived science.