Explain, in your own words, how entropy is used in statistical physics.

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The principle of increasing entropy Entropy principle: "For all irreversible processes, the change in entropy of the universe is positive." To prove the principle can be taken the case of reversible adibatic process. AS = Sf - Si Prove that the entropy of the universe is positive: E4S 2 0

One of the statements of the second law is that “heat cannot flow from a colder body to awarmer one without external aid”. Assume two systems, 1 and 2, at T1 and T2 (whereT2 > T1 ). Show that if a quantity of heat q did flow spontaneously from 1 to 2, the processwould result in a decrease in the entropy of the universe. [You may assume that the heat flowsso slowly that the process can be regarded as reversible. Assume also that the loss of heat bythe system 1 and the gain of heat by 2 do not affect T1 and T2 .]

(a) What is the unit of "specific entropy"? Is it an extensive property? (b) What is an isentropic process? Please give an example. (c) Explain the increase of entropy principle. (d) The entropy of a hot baked pizza decreases as it cools. Is this a violation of the increase of entropy principle? Explain.

Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length L Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first link to the end of the last link. Using the thermodynamic identity, you can now express the tension force F in terms of a partial derivative of the entropy. From this expression, compute the tension in terms of L, T , N, and l.

Suppose that 10 distinguishable particles are equipartitioned in a container that has 100 equal-sized compartments. What is the entropy on this system?