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Chapter 1: 1.19. (page 13)
Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecule are moving faster, on average? By what factor?
In thermal equilibrium, hydrogen molecules moves faster by a factor of 4
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A hiker wishes to climb to the summit of Mt. Ogden, an ascent ofvertical feet .
Assuming that she is efficient at converting chemical energy from food into mechanical work, and that essentially all the mechanical work is used to climb vertically, roughly how many bowls of corn flakes (standard serving size ounce, kilocalories) should the hiker eat before setting out?
As the hiker climbs the mountain, three-quarters of the energy from the corn flakes is converted to thermal energy. If there were no way to dissipate this energy, by how many degrees would her body temperature increase?
In fact, the extra energy does not warm the hiker's body significantly; instead, it goes (mostly) into evaporating water from her skin. How many liters of water should she drink during the hike to replace the lost fluids? (At, a reasonable temperature to assume, the latent heat of vaporization of water is more than atrole="math" localid="1650290792399" ).
According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)
Imagine some helium in a cylinder with an initial volume of and an initial pressure of Somehow the helium is made to expand to a final volume of ,in such a way that its pressure rises in direct proportion to its volume.
(a) Sketch a graph of pressure vs. volume for this process.
(b) Calculate the work done on the gas during this process, assuming that there are no "other" types of work being done.
(c) Calculate the change in the helium's energy content during this process.
(d) Calculate the amount of heat added to or removed from the helium during this process.
(e) Describe what you might do to cause the pressure to rise as the helium expands.
Does it ever make sense to say that one object is "twice as hot" as another? Does it matter whether one is referring to Celsius or Kelvin temperatures? Explain.
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.
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