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Chapter 3: Q. 3.9 (page 95)
In solid carbon monoxide, each CO molecule has two possible orientations: CO or OC. Assuming that these orientations are completely random (not quite true but close), calculate the residual entropy of a mole of carbon monoxide.
The residual entropy for a carbon monoxide is calculated to be.
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The results of either of the two preceding problems can also be applied to the vibrational motions of gas molecules. Looking only at the vibrational contribution to the heat capacity graph for shown in Figure 1.13, estimate the value of for the vibrational motion of an molecule.
When the sun is high in the sky, it delivers approximately 1000 watts of power to each square meter of earth's surface. The temperature of the surface of the sun is about , while that of the earth is about .
(a) Estimate the entropy created in one year by the flow of solar heat onto a square meter of the earth.
(b) Suppose you plant grass on this square meter of earth. Some people might argue that the growth of the grass (or of any other living thing) violates the second law of thermodynamics, because disorderly nutrients are converted into an orderly life form. How would you respond?
Starting with the result of Problem 2.17, find a formula for the temperature of an Einstein solid in the limit . Solve for the energy as a function of temperature to obtain (where is the size of an energy unit).
Consider an Einstein solid for which both N and q are much greater than . Think of each oscillator as a separate "particle."
(a) Show that the chemical potential is
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(b) Discuss this result in the limits and , concentrating on the question of how much increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?
Estimate the change in the entropy of the universe due to heat escaping from your home on a cold winter day.
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