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Chapter 12: Q4Q (page 507)
Explain why it is a disadvantage for some purposes that the specific heat of all materials decreases a low temperature.
The temperature increases very fast when adding to the specific heat substance.
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At room temperature (293 K), calculate in joules and eV.
Figure 12.57 shows a one-dimensional row of 5 microscopic objects each of mass , connected by forces that can be modeled by springs of stiffness 15 N/m. These objects can move only along the x axis.
(a) Using the Einstein model, calculate the approximate entropy of this system for total energy of 0, 1, 2, 3, 4, and 5 quanta. Think carefully about what the Einstein model is, and apply those concepts to this one-dimensional situation. (b) Calculate the approximate temperature of the system when the total energy is 4 quanta. (c) Calculate the approximate specific heat on a per-object basis when the total energy is 4 quanta. (d) If the temperature is raised very high, what is the approximate specific heat on a per-object basis? Give a numerical value and compare with your result in part (c).
A block of copper at a temperature of is placed in contact with a block of aluminium at a temperature of 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 . (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?
There was transfer of energy of 5000 J into a system due to a temperature difference, and the entropy increased by 10 J/K. What was the approximate temperature of the system, assuming that the temperature didn’t change very much?.
Verify that this equation gives the correct number of ways to arrange 0, 1, 2, 3, or 4 quanta among 3 one-dimensional oscillators, given in earlier tables (1, 3, 6, 10, 15).
Q1 | Q2 | #ways1 | #ways2 | #ways1 #ways2 |
0 | 4 | 1 | 15 | 15 |
1
| 3
| 3
| 10 | 30 |
2 | 2
| 6
| 6
| 36 |
3
| 1
| 10
| 3
| 30 |
4
| 0
| 15
| 1
| 15 |
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