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Chapter 12: Entropy: Limits on the Possible

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Matter & Interactions
Pages: 472 - 512
Matter & Interactions

Matter & Interactions

Book edition 4th edition
Author(s) Ruth W. Chabay, Bruce A. Sherwood
Pages 1135 pages
ISBN 9781118875865

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Illustration

49 Questions for Chapter 12: Entropy: Limits on the Possible

  1. A gas is made up of diatomic molecules. At temperature T1,the ratio of the number of molecules in vibrational energy state 2to the number of molecules in the ground state is measured, andfound to be 0.35. The difference in energy between state 2 andthe ground state is ΔE. (a) Which of the following conclusions is

    Found on Page 507

  2. This question follows the entire chain of reasoning involved in determining the specific heat of an Einstein solid. Start with two metal blocks, one consisting of one mole of aluminum (27 g) and the other of one mole of lead (207 g), both initially at a temperature very near absolute zero (0 K). From measurements of Young’s modulus one finds that the effective stiffness of the interatomic bond modeled as a spring is 16N/mfor aluminum and 5 N/m for lead. (a) Is the number of quantized oscillators in the aluminum block greater, smaller, or the same as the number in the lead block? (b) What is the initial entropy of each block? (c) In which metal is the energy spacing of the quantized harmonic oscillators larger? (d) If we add 1 J of energy to each block, which metal now has the larger number of energy quanta? (e) In which block is the number of possible ways of arranging this of energy greater? (f) Which block now has the larger entropy? (g) Which block experienced a greater entropy change? (h) Which block experienced the larger temperature change? (i) Which metal has the larger specific heat at low temperatures? (j) Does your conclusion agree with the actual data given in Figure 12.33? (The numerical data are given in a table accompanying Problem P64.)

    Found on Page 472

  3. The reasoning developed for counting microstates applies to many other situations involving probability. For example, if you flip a coin 5 times, how many different sequences of 3 heads and 2 tails are possible? Answer: 10 different sequences, such as HTHHT or TTHHH. In contrast, how many different sequences of 5 heads and 0 tails are possible? Obviously only one, HHHHH, and our equation gives 5!/[5!0!]=1, using the standard definition that 0! is defined to equal 1.

    Found on Page 508

  4. The reasoning developed for counting microstates applies to many other situations involving probability. For example, if you flip a coin 5 times, how many different sequences of 3 heads and 2 tails are possible? Answer: 10 different sequences, such as HTHHT or TTHHH. In contrast, how many different sequences of 5 heads and 0 tails are possible? Obviously only one, HHHHH, and our equation gives , using the standard definition thatis defined to equal 1.

    Found on Page 472

  5. Suppose that the entropy of a certain substance (not anEinstein solid) is given byS=aE, where ais a constant. Whatis the energy Eas a function of the temperature T?

    Found on Page 509

  6. Suppose that the entropy of a certain substance (not anEinstein solid) is given by S=aE, where ais a constant. Whatis the specific heat capacity Cas a function of the temperature T?

    Found on Page 509

  7. At sufficiently high temperatures, the thermal speeds of gas molecules may be high enough that collisions may ionize a molecule (that is, remove an outer electron). An ionized gas in which each molecule has lost an electron is called a “plasma.” Determine approximately the temperature at which air becomes a plasma.

    Found on Page 511

  8. Explain what it means for something to have wavelike properties; for something to have particulate properties. Electromagnetic radiation can be discussed in terms of both particles and waves. Explain the experimental verification for each of

    Found on Page 507

  9. Explain qualitatively the basis for the Boltzmann distribution. Never mind the details of the math for the moment. Focus on the trade-offs involved with giving energy to a single oscillator vs. giving that energy to a large object.

    Found on Page 507

  10. Many chemical reactions proceed at rates that depend on the temperature. Discuss this from the point of view of the Boltzmann distribution.

    Found on Page 507

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