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Chapter 12: Q43P (page 510)
At room temperature (293 K), calculate in joules and eV.
The value of is and the value ofeV is role="math" localid="1657860404123" .
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A microscopic oscillator has its first and second excited states and above the ground-state energy. Calculate the Boltzmann factor for the ground state, first excited state, and second excited state, at room temperature.
The interatomic spring stiffness for tungsten is determined from Young’s modulus measurements to be 90 N. The mass of one mole of tungsten is 0185 kg . If we model a block of tungsten as a collection of atomic “oscillators” (masses on springs), note that since each oscillator is attached to two “springs,” and each “spring” is half the length of the interatomic bond, the effective interatomic spring stiffness for one of these oscillators is 4 times the calculated value given above.Use these precise values for the constants: (Planck’s constant divided by 2π), Avogadro’s number = , (the Boltzmann constant). (a) What is one quantum of energy for one of these atomic oscillators? (b) Figure 12.56 contains the number of ways to arrange a given number of quanta of energy in a particular block of tungsten. Fill in the blanks to complete the table, including calculating the temperature of the block. The energy E is measured from the ground state. Nothing goes in the shaded boxes. Be sure to give the temperature to the nearest 0.1 kelvin. (c) There are about 60 atoms in this object. What is the heat capacity on a per-atom basis? (Note that at high temperatures the heat capacity on a per-atom basis approaches the classical limit of 3kB = 4.2×10−23 J/K/atom.)
In an insulated container an 100 W electric heating element of small mass warms up a 300 g sample of copper for 6 s. The initial temperature of the copper was (roomtemperature). Predict the final temperature of the copper, using the 3kB specific heat per atom.
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.
Suppose that you look once every second at a system with oscillators and energy quanta, to see whether your favorite oscillator happens to have all the energy (all quanta) at the instant you look. You expect that just once out ofrole="math" localid="1655710247969" times you will find all of the energy concentrated on your favorite oscillator. On the average, about how many years will you have to wait? Compare this to the age of the Universe, which is thought to be aboutrole="math" localid="1655710262469" years.role="math" localid="1655710345899"
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