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Chapter 12: Q8CP (page 497)
At room temperature, show that KBT≈1/ 40 eV. It is useful to memorize this result, because it tells a lot about what phenomena are likely to occur at room temperature.
The result can be proved using the energy equation.
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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 for 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.)
A block of copper (one mole has a mass of 63.5 g ) at a temperature of is put in contact with a 100 gblock of aluminum (molar mass 27 g) at a temperature of. The blocks are inside an insulated enclosure, with little contact with the walls. At these temperatures, the high-temperature limit is valid for the specific heat. Calculate the final temperature of the two blocks. Do NOT look up the specific heats of aluminum and copper; you should be able to figure them out on your own.
How many different ways are there to arrange 4 quanta among 3 atoms in a solid?
Calculate the escape speed from the Moon and compare with typical speeds of gas molecules. The mass of the Moon is, and its radius is .
How many different ways are there to get 5 heads in 10 throws of a true coin? How many different ways are there to get no heads in 10 throws of a true coin?
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