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Chapter 12: Q2Q (page 507)

What is the advantage of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms (natural logarithm of the number of microstates)?

Short Answer

Expert verified

The advantage of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms (natural logarithm of the number of microstates) is that the natural logarithms are used to express large numbers.

Step by step solution

01

Significance of natural logarithm

There are 3 reasons for finding a natural logarithm.

  • A quantity “e”that happens frequently and unavoidably in nature.
  • Natural logarithms consist of simple derivativesamong all the other logarithms.
  • While calculating logarithms to the base, we first need to calculate “e” andmultiply it by a constant.
02

Step 2: Advantages of plotting the (natural) logarithm

The following are the advantages of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms;

  • The natural logarithm can be moderately skeweddata more generally distributed to constant variance.
  • We have to use astraight line to allow the data to fall in a curved pattern to be generated.
  • We canexpress large numbersby using natural logarithms.

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Most popular questions from this chapter

Young’s modulus for copper is measured by stretching a copper wire to be about 1.2×1011N/m2. The density of copper is about 9g/cm3, and the mass of a mole is .Starting from a very low temperature, use these data to estimate roughly the temperature T at which we expect the specific heat for copper to approach 3 kB . Compare your estimate with the data shown on a graph in this chapter.

A block of copper at a temperature of 50°C is placed in contact with a block of aluminium at a temperature of45°C in an insulated container. As a result of a transfer of 2500 J of energy from the copper to the aluminium, the final equilibrium temperature of the two blocks is 48°C. (a) What is the approximate change in the entropy of the aluminium block? (b) What is the approximate change in the entropy of the copper block? (c) What is the approximate change in the entropy of the Universe? (d) What is the change in the energy of the Universe?

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