What is expression for entropy?

Question

I am confused with this HW assignment:

The entropy of a system is found by placing a sign -in front of sign Σ in front of products of thingies P_i and their logarithms. Using letter S for entropy and denoting logarithms by ln() write an expression for the entropy of the system.

I figured out that the beginnig should look like
S = -Σ
but logarithms took me completely off guard. What are those logarithms things anyway.

I need to know, because I am finishing my MS in physics and plan to develop tubines for airplane engines.

Answer 1

Seeminlgy, you studied physics in such terms as in this link?

http://answers.yahoo.com/question/index?qid=20071211132536AALgPBt

This is bad teaching. It is not explained, for example, that the square of the velocity V is obtained by placing small digit "2" in the upper-right side from V, and that taking one-half actually means placing the character "/ " followed by digit "2" after the expression. Students should get clear instructions, which do not admit any misinterpretation.

Now, I am not surprised that a future developer of turbines for airplane engines does not know what the logarithm is. This is a composite function derived by operating with "n" first and then with "l" on a number. Usually, both "l" and "n" are placed on the same button in a calculator, which looks like "ln". This allows you to execute the composite "ln" function with two clicks (do not forget to click the number first). What might be confusing, is that there are two other similar looking buttons: "log" and "Inv". To distinguish between them, you should count characters. Only the "right" logarithm consists of two characters, which are separated by a small gap.

Try to memorize scientific concepts in terms of sequences of buttons in your calculator, which you need to press to get the desired result. For example: "to find the logarithm - press the big red buton AC, then the second button from the left hand (most likely this is the hand where you wear watch) side in the upper row, then ... etc". Simple and clear. Ask you professor, if you are not sure. Then the engines will be powerful and the airplanes fast.

I am checking buttons in my calculator, and still cannot find the "P_i" button. Did you type this thingie correctly?

Answer 2

Classical thermodynamics and Statistical Mechanics looks at entropy in different ways. In the former, entropy is defined to be

dS = dQ/T

where dQ is change in heat in a system, and this is where you might find a lot of Σs because you're trying to account for all the heat flows, which is added linearly.

However, the latter defines it to be:

S = k In(Ω)

where k is the Botlzman constant, and Ω (god, I always wanted the chance to use this symbol here) is the number of equally available microstates in a system. This time, however, you see the product symbol Π in computing this number Ω, not summation. Pay respect to this tiny equation, because Boltzman thought so much of it that he had it carved in his tombstone--his life's work.

Answer 3

"concept" created the concept-approximately "entropy". that's a human convention to describe randomness. concept can organize issues against entropy ( affliction ) and consequently opposite it ( a minimum of temporarily ). if we human beings will ever grasp the universe and can opposite entropy completely via using our concept, then we are able to ought to alter the concept-approximately entropy itself to adventure our observations ! to respond to your question, concept is anti-entropy !

Answer 4

Why don't you go for the PhD? You're smart enough.