Chapter 20: Q79P (page 608)
In a real refrigerator, the low-temperature coils are at , and the compressed gas in the condenser is at . What is the theoretical coefficient of performance?
The theoretical coefficient of performance is 6.67
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A Carnot refrigerator extracts 35.0 kJ as heat during each cycle, operating with a coefficient of performance of 4.60 . What are (a) the energy per cycle transferred as heat to the room and (b) the work done per cycle?
Energy can be removed from water as heat at and even below the normal freezing point (at atmospheric pressure) without causing the water to freeze; the water is then said to be supercooled. Suppose a 1.00 gwater drop is super-cooled until its temperature is that of the surrounding air, which is at. The drop then suddenly and irreversibly freezes, transferring energy to the air as heat. What is the entropy change for the drop? (Hint: Use a three-step reversible process as if the water were taken through the normal freezing point.) The specific heat of ice is.
An inventor has built an engine X and claims that its efficiency X is greater than the efficiency of an ideal engine operating between the same two temperatures. Suppose you couple engine X to an ideal refrigerator (Fig. 20-34a) and adjust the cycle of engine X so that the work per cycle it provides equals the work per cycle required by the ideal refrigerator. Treat this combination as a single unit and show that if the inventor’s claim were true, the combined unit would act as a perfect refrigerator (Fig. 20-34b), transferring energy as heat from the low-temperature reservoir to the high-temperature reservoir without the need for work.
A box contains Nmolecules. Consider two configurations: Configuration Awith an equal division of the molecules between the two halves of the box, and configuration Bwith 60.0%of the molecules in the left half of the box and 40.0%in the right half. For N =50, what are (a) the multiplicity WAof configuration A, (b) the multiplicity of configuration B, and (c) the ratioof the time the system spends in configuration Bto the time it spends in configuration A? For N =100, what are (d), (e), and (f)? ForN =200, what are (g), (h), and (i)? ( j) With increasingN, doesincrease, decrease, or remain the same?
As a sample of nitrogen gas (N2) undergoes a temperature increase at constant volume, the distribution of molecular speeds increases. That is, the probability distribution function P(v)for the molecules spreads to higher speed values, as suggested in Fig. 19-8b. One way to report the spread in P(v)is to measure the difference between the most probable speedand the rms speed. When P(v) spreads to higher speeds, increases. Assume that the gas is ideal and the N2 molecules rotate but do not oscillate. For 1.5 mol, an initial temperature of 250 K, and a final temperature of 500 K, what are (a) the initial difference, (b) the final difference,, and (c) the entropy change for the gas?
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