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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

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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

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 .

Fill in the algebraic steps to derive the Sackur-Tetrode equation(2.49).

Write e1023in the form 10x, for somex.

Using the same method as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, Aand B, whose relative proportion is arbitrary. Let Nbe the total number of molecules and letx be the fraction of these that are of speciesB . You should find

ΔSmixing=Nk[xlnx+(1x)ln(1x)]

Check that this expression reduces to the one given in the text whenx=1/2 .

The natural logarithm function, ln, is defined so that elnx=xfor any positive numberx.
aSketch a graph of the natural logarithm function.
b Prove the identities
localid="1650331641178" lnab=lna+lnbandlocalid="1650331643409" lnab=blna
(c) Prove thatlocalid="1650331645612" ddxlnx=1x.
(d) Derive the useful approximation

localid="1650331649052" ln(1+x)x

which is valid when localid="1650331651790" |x|1. Use a calculator to check the accuracy of this approximation for localid="1650331654235" x=0.1and localid="1650331656447" x=0.01.

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