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Chapter 12: Q18P (page 508)
How many different ways are there to arrange 4 quanta among 3 atoms in a solid?
The numbers of ways to arrange 4 quanta among 12 oscillations is 1,365.
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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 鈥減lasma.鈥� Determine approximately the temperature at which air becomes a plasma.
For a certain metal the stiffness of the interatomic bond and the mass of one atom are such that the spacing of the quantum oscillator energy levels is J. A nanoparticle of this metal consisting of atoms has a total thermal energy of role="math" localid="1657867970311" J. (a) What is the entropy of this nanoparticle? (b) The temperature of the nanoparticle is 87 K. Next we add J to the nanoparticle. By how much does the entropy increase?
The entropy S of a certain object (not an Einstein solid) is the following function of the internal energy , where b is a constant. (a) Determine the internal energy of this object as a function of the temperature.
(b) What is the specific heat of this object as a function of the temperature?
A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator areapart. (a) When the nanoparticle鈥檚 energy is in the rangeJ to, what is the approximate temperature? (In order to keep precision for calculating the specific heat, give the result to the nearest tenth of a kelvin.) (b) When the nanoparticle鈥檚 energy is in the rangerole="math" localid="1657107429075" to, what is the approximate temperature? (In order to keep precision for calculating the specific heat, give the result to the nearest tenth of a degree.) (c) When the nanoparticle鈥檚 energy is in the rangeto, what is the approximate heat capacity per atom? Note that between parts (a) and (b) the average energy increased from 5.5 quanta to 8.5 quanta. As a check, compare your result with the high temperature limit of .
Explain why it is a disadvantage for some purposes that the specific heat of all materials decreases a low temperature.
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