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Chapter 1: Q. 1.24 (page 17)
Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).
Total thermal energy is 35.3 J.
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Consider the combustion of one mole of methane gas:
The system is at standard temperature and pressure both before and after the reaction.
(a) First imagine the process of converting a mole of methane into its elemental constituents (graphite and hydrogen gas). Use the data at the back of this book to find for this process.
(b) Now imagine forming a mole of and two moles of water vapor from their elemental constituents. Determine for this process.
(c) What is for the actual reaction in which methane and oxygen form carbon dioxide and water vapor directly? Explain.
(d) How much heat is given off during this reaction, assuming that no "other" forms of work are done?
(e) What is the change in the system's energy during this reaction? How would your answer differ if theended up as liquid water instead of vapor?
(f) The sun has a mass ofand gives off energy at a rate of watts. If the source of the sun's energy were ordinary combustion of a chemical fuel such as methane, about how long could it last?
By applying Newton’s laws to the oscillations of a continuous medium, one can show that the speed of a sound wave is given by
,
where is the density of the medium (mass per unit volume) and B is the bulk modulus, a measure of the medium’s stiffness? More precisely, if we imagine applying an increase in pressure to a chunk of the material, and this increase results in a (negative) change in volume , then B is defined as the change in pressure divided by the magnitude of the fractional change in volume:
This definition is still ambiguous, however, because I haven't said whether the compression is to take place isothermally or adiabatically (or in some other way).
An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in the given figure.
Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are "frozen out." Also assume that the only type of work done on the gas is quasistatic compression-expansion work.
(a) For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of . (Hint: Compute before Q, using the ideal gas law and the equipartition theorem.)
(b) Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.
(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.
The enthalpy of combustion of a gallon ( liters) of gasoline is about . The enthalpy of combustion of an ounce of corn flakes is about. Compare the cost of gasoline to the cost of corn flakes, per calorie.
Uranium has two common isotopes, with atomic masses of 238 and 235. One way to separate these isotopes is to combine the uranium with fluorine to make uranium hexafluoride gas, UF6, then exploit the difference in the average thermal speeds of molecules containing the different isotopes. Calculate the rms speed of each type of molecule at room temperature, and compare them.
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