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Chapter 12: Q20P (page 508)
In order to calculate the number of ways of arranging a given amount of energy in a tiny block of copper, the block is modeled as containing independent oscillators. How many atoms are in the copper block?
atoms are in the copper block.
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Suppose that the entropy of a certain substance (not anEinstein solid) is given by, where ais a constant. Whatis the energy Eas a function of the temperature T?
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’s 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’s 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’s 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 .
In Chapter 4 you determined the stiffness of the interatomic “spring” (chemical bond) between atoms in a block of lead to be 5 N/m, based on the value of Young’s modulus for lead. Since in our model each atom is connected to two springs, each half the length of the interatomic bond, the effective “interatomic spring stiffness” for an oscillator is
4 × 5 N/m = 20 N/m. The mass of one mole of lead is 207 g (0.207 kg). What is the energy, in joules, of one quantum of energy for an atomic oscillator in a block of lead?
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.
How does the speed of sound in a gas change when you raise the temperature from ? Explain briefly.
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