Bite-sized assorted physics QnA.

Want to read something "physicsy" but without too much math? I am happy to oblige, here are some assorted short conceptual questions and my only slightly longer answers from Physics Stack Exchange.

Q. When two reserviors exchange heat, it is considered as reversible heat transfer and entropy is calculated.

But when the process is reversible change in entropy of universe must be zero. But why positive value is coming?

A. Great conceptual question. That process is most definitely irreversible. But when we calculate the entropy change for each reservoir separately, we use a cool trick: for the purposes of calculating the entropy change we can replace an irreversible process with a reversible process having the same initial and final states.

Why does the trick work? Because entropy is a state function, so its change only depends on the initial and final states.

So how does this work, for example, for the colder reservoir? We just replace the actual process of heat absorption with a very slow, gradual, addition of heat, making sure the reservoir always stays in thermal equilibrium. That new process is reversible (we can always very slow, gradually, take the heat out), and so we can calculate the entropy change for that reservoir by integrating $\frac{dQ}{T}$.

Q. If we compute the number of microstates in a black-hole of Planck radius using the Bekenstein–Hawking (BH) formula for the entropy we get $n~=~\exp(Entropy)~=~\exp(\pi/4)$. Is there a physical interpretation for non-integer numbers of microstates?

A. Two points:

1. There is no clear physical interpretation for a non-integer number of microstates.

Why not? Because for a quantum system the space of possible states is a vector space. When we talk about the number of microstates, we are referring to the dimensionality of that vector space (or subspace), which is an integer.

2. The entropy is not necessarily the logarithm of the number of microstates.

That's only true if the microstates are equally likely. But in general, even though the number of microstates is an integer, the entropy is not necessarily the logarithm of an integer.

Q. In a series circuit, the voltage is the same everywhere on that circuit. However, thinking about Voltage as a steady force or potential, I imagine that at parts of the circuit without resistance, the current would be greater as the force would be able to move them faster, without any obstruction. Why is this not the case?

A. The situation is completely analogous to that of a water pipe of uneven thickness (horizontal, so we can ignore gravity), with voltage being analogous to pressure. If the current through any part "tried" to increase (compared to the current in a neighboring part), it would create a buildup of charge (water molecule concentration in our pipe analogy), which would alter the voltage (pressure) gradient and make it slow down again.

For that reason a condition of unequal current can't persist for too long. Which means that in the normal, steady state situation (same current everywhere), the voltage (pressure) gradient varies along the path, to "enforce" the condition of the equal current in order to "compensate" for the fact that it's easier for the current to flow through some parts (low resistance/wider pipe) than through others.

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