There are many different definitions and metaphors for entropy. To name just a f
ID: 1530212 • Letter: T
Question
There are many different definitions and metaphors for entropy. To name just a few examples, entropy can be described in terms of: microstates; irreversibility; disorder; heat transfer (delta Q/T); energy spreading; information; useful work. Choose a physical system or process (either from this class or not), and use two different definitions/metaphors for entropy to describe whats happening in this system/process. Then explain how these two descriptions are consistent with each other. There are many phenomena in nature that fall off exponentially with some variable. For example, at large distances from the nucleus, an electron cloud in an atom or molecule looks like a fuzzy ball of charge with charge density proportional to e^-or where r is the distance from the nucleus and a is a parameter with units o' inverse distance. If curves A and B in the figure at the right represent two such charge distributions, which one has the larger value of a? Explain how you decided. For a radioactive material, the number of atoms of a radioactive element decreases like N(t) = N_0 e^-t/tau where N_0 is the number of atoms of that element present at time t = 0 and t is a parameter with units of time representing the time it takes for the number of atoms to decrease by a factor of 1/e. Two radioactive materials start at time t = 0 with the same number of atoms. The graphs at the right show how their numbers fall with time. Which element, A or B, has the larger value of t?Explanation / Answer
Answer of Q-3:
In classical thermodynamics, change in entropy is defined as the change in heat energy multiplied by inverse of absolute temperature. This is a reversible case. But in the universe entropy is always increasing. And absolute value of entropy can be measured by using third law of thermodynamics, which states that S = 0 at absolute zero. The concept of entropy has come from Carnot cycle which gives us that entropy is always increasing, i.e., the entropy that leaves the system is greater than that which enters. So entropy is an irriversible process; and to measure its value we consider it as a riversible one. this is all about the entropy in macroscopic thermodynamics.
In stastical mechanics entropy gives us a deeper understanding. Here entropy is the measure of uncertainty. And it is proportional to natural logarithim of number of microstates which is ameasure of disorder if the system.
Answer of Q-4:
For curve A the value of "a" is greater. as the curves are charge vs distance, term above exponent will greater for greater value of "a". and due to negative singn before it and whole exponent term decreases more rapidly.
Answer of Q-5;
opposite case of the previous problem. Here we can consider tao as inverse of "a" . So greater value of tao less value of exponent. So its decrease will be slower. Correct answer is elemint A which has larger value of tao.
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