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Chapter 15: Q30CQ (page 549)
Does a gas become more orderly when it liquefies? Does its entropy change? If so, does the entropy increase or decrease? Explain your answer.
As a gas liquefies into a liquid, the entropy decreases.
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The temperature of a rapidly expanding gas decreases. Explain why in terms of the first law of thermodynamics. (Hint: Consider whether the gas does work and whether heat transfer occurs rapidly into the gas through conduction.)
A\({\bf{4}}\)-ton air conditioner removes\({\bf{5}}.{\bf{06}} \times {\bf{1}}{{\bf{0}}^{\bf{7}}}\;{\bf{J}}\)(\({\bf{48}},{\bf{000}}\)British thermal units) from a cold environment in\({\bf{1}}.{\bf{00}}\;{\bf{h}}\). (a) What energy input in joules is necessary to do this if the air conditioner has an energy efficiency rating ( EER) of\({\bf{12}}.{\bf{0}}\)? (b) What is the cost of doing this if the work costs\({\bf{10}}.{\bf{0}}\)cents per\({\bf{3}}.{\bf{60}} \times {\bf{1}}{{\bf{0}}^{\bf{6}}}\;{\bf{J}}\)(one kilowatt-hour)? (c) Discuss whether this cost seems realistic. Note that the energy efficiency rating ( EER) of an air conditioner or refrigerator is defined to be the number of British thermal units of heat transfer from a cold environment per hour divided by the watts of power input.
A woman shuts her summer cottage up in September and returns in June. No one has entered the cottage in the meantime. Explain what she is likely to find, in terms of the second law of thermodynamics.
(a) If tossing 100 coins, how many ways (microstates) are there to get the three most likely macrostates of 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails? (b) What percent of the total possibilities is this? (Consult Table 15.4.)
Is a uniform-temperature gas more or less orderly than one with several different temperatures? Which is more structured? In which can heat transfer result in work done without heat transfer from another system?
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