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Chapter 2: Q. 2.41 (page 83)

Describe a few of your favorite, and least favorite, irreversible processes. In each case, explain how you can tell that the entropy of the universe increases.

Short Answer

Expert verified

The entropy of the universe increases an example of irreversible processes are

Allowing a hot cup of tea to cool on its own and an egg that has fallen on the floor and cracked open, spilling its contents and in general, anything that cannot occur spontaneously in a time-reversed form is irreversible. If you leave a cup of tea alone, it will never heat up. A broken egg, likewise, will never rejoin itself.

Step by step solution

01

Step: 1 Definition of irreversible process in entropy:

The overall energy of the system and its environment grows when an irreversible event occurs. To establish whether or not a hypothetical process is reversible, the second law of thermodynamics can be applied. When there's no dissipation, a process appears to be reversible.The entropy of the cosmos remains unaltered in a reversible process, whereas the entropy of the universe grows in an irreversible process. It also rises when a quantifiable non-spontaneous process occurs. Because energy continually goes downward, entropy increases.

02

Step: 2 Example of irreversible process:

The entropy of the universe increases an example of irreversible processes are:
1Allowing a hot cup of tea to cool on its own.

2An egg that has fallen on the floor and cracked open, spilling its contents.

3In general, anything that cannot occur spontaneously in a time-reversed form is irreversible. If you leave a cup of tea alone, it will never heat up. A broken egg, likewise, will never rejoin itself.

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Most popular questions from this chapter

Use a computer to plot formula 2.22directly, as follows. Define z=q_{A}/q, so that (1-z)=q_{B}/q. Then, aside from an overall constant that we'll ignore, the multiplicity function is [4z(1-z)]N, where zranges from 0to1and the factor of 4ensures that the height of the peak is equal to 1for any N. Plot this function forN=1,10,100,1000, and 10,000. Observe how the width of the peak decreases asNincreases.

How many possible arrangements are there for a deck of 52playing cards? (For simplicity, consider only the order of the cards, not whether they are turned upside-down, etc.) Suppose you start w e in the process? Express your answer both as a pure number (neglecting the factor of k) and in SI units. Is this entropy significant compared to the entropy associated with arranging thermal energy among the molecules in the cards?

For either a monatomic ideal gas or a high-temperature Einstein solid, the entropy is given by times some logarithm. The logarithm is never large, so if all you want is an order-of-magnitude estimate, you can neglect it and just say . That is, the entropy in fundamental units is of the order of the number of particles in the system. This conclusion turns out to be true for most systems (with some important exceptions at low temperatures where the particles are behaving in an orderly way). So just for fun, make a very rough estimate of the entropy of each of the following: this book (a kilogram of carbon compounds); a moose of water ; the sun of ionized hydrogen .

A black hole is a region of space where gravity is so strong that nothing, not even light, can escape. Throwing something into a black hole is therefore an irreversible process, at least in the everyday sense of the word. In fact, it is irreversible in the thermodynamic sense as well: Adding mass to a black hole increases the black hole's entropy. It turns out that there's no way to tell (at least from outside) what kind of matter has gone into making a black hole. Therefore, the entropy of a black hole must be greater than the entropy of any conceivable type of matter that could have been used to create it. Knowing this, it's not hard to estimate the entropy of a black hole.
aUse dimensional analysis to show that a black hole of mass Mshould have a radius of order GM/c2, where Gis Newton's gravitational constant and cis the speed of light. Calculate the approximate radius of a one-solar-mass black holeM=2×1030kg .
bIn the spirit of Problem 2.36, explain why the entropy of a black hole, in fundamental units, should be of the order of the maximum number of particles that could have been used to make it.

cTo make a black hole out of the maximum possible number of particles, you should use particles with the lowest possible energy: long-wavelength photons (or other massless particles). But the wavelength can't be any longer than the size of the black hole. By setting the total energy of the photons equal toMc2 , estimate the maximum number of photons that could be used to make a black hole of mass M. Aside from a factor of 8π2, your result should agree with the exact formula for the entropy of a black hole, obtained* through a much more difficult calculation:

Sb.h.=8π2GM2hck

d Calculate the entropy of a one-solar-mass black hole, and comment on the result.

Suppose you flip1000 coins.
a What is the probability of getting exactly 500heads and 500tails? (Hint: First write down a formula for the total number of possible outcomes. Then, to determine the "multiplicity" of the 500-500"macrostate," use Stirling's approximation. If you have a fancy calculator that makes Stirling's approximation unnecessary, multiply all the numbers in this problem by 10, or 100, or1000, until Stirling's approximation becomes necessary.)
bWhat is the probability of getting exactly 600heads and400 tails?
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