In case you cannot read it: Bigger picture. Briefly answer the following: With a
ID: 1699546 • Letter: I
Question
In case you cannot read it:
Briefly answer the following: With an example, explain the difference between a microstate and a macrostate. Let a, b be two accessible microstates. Is it correct to say that the system can go from a rightarrow b just as likely as from b rightarrow a? Let X, Y be two macrostates of a system. Is it okay to assume that the system can change from X rightarrow Y just as likely as from Y rightarrow X? What is the change of entropy in a quasi-static, reversible process? Does the second law of thermodynamics require that, the entropy of everything in the universe to increase? If you increase the multiplicity by a factor of 10, how much does the scaled entropy, S/k, change? Comparing some crushed ice and a glass of water of same mass, which appears more disorderly? Which has more entropy? A negative temperature is supposed to be hotter than any positive temperature. Can we keep adding energy to an ideal gas until it is so hot that its temperature becomes negative? Since T = U/ S and a thermometer can measure the temperature, does it mean that a thermometer hits intelligence and knows calculus? (Be sure to give an intelligent answer!)
Explanation / Answer
a) A microstate of our system is a detailed specification of the state (h or t)
of each of the N coins: e.g., hhhh . . . hhh, or hthhthtth . . . ht, and so on.
In other words, each “word” of N letters, made up of just the two letters h
and t, is a possible microstate of our system.
A macrostate of the system is specified as follows. Let H and T denote
the total number of heads and tails, respectively, in the collection. Then
the pair of values (H, T) specifies a macrostate of the system. Clearly, in
general, a knowledge of H and T is not sufficient to tell us whether any
particular coin is in the h state or the t state. It is therefore obvious that
a macrostate of the system provides much less detailed information about
the system than a microstate does. Equivalently, much less information is
necessary to specify a macrostate.
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b) No, because in microstate the properties of a and b are different .
c) Yes
Macrostate is the collection of microstates. So all macrostates are having the same properties.
d) The change in entropy in quasi static and reversible process is zero.
e) No , because in adiabatic process the change in heat is zero , so the entropy is zero.
f ) Entropy S =k ln
Here = 10
S = k ln(10)
s/k = 2.302585
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