Chapter 20: Problem 17
Why might a heat pump have an advantage over a space heater that converts electrical energy directly into thermal energy?
Chapter 20: Problem 17
Why might a heat pump have an advantage over a space heater that converts electrical energy directly into thermal energy?
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Get started for freeThe entropy of a macroscopic state is given by \(S=k_{B} \ln w,\) where \(k_{B}\) is the Boltzmann constant and \(w\) is the number of possible microscopic states. Calculate the change in entropy when \(n\) moles of an ideal gas undergo free expansion to fill the entire volume of a box after a barrier between the two halves of the box is removed.
When a coin is tossed, it can land heads up or tails up. You toss a coin 10 times, and it comes up heads every time. What is the probability that the coin will come up heads on the 11 th toss? a) \(10 \%\) c) 5096 e) \(100 \%\) b) \(20 \%\) d) \(90 \%\)
A heat pump has a coefficient of performance of \(5.00 .\) If the heat pump absorbs 40.0 cal of heat from the cold outdoors in each cycle, what is the amount of heat expelled to the warm indoors?
Suppose a person metabolizes \(2000 .\) kcal/day. a) With a core body temperature of \(37.0^{\circ} \mathrm{C}\) and an ambient temperature of \(20.0^{\circ} \mathrm{C}\), what is the maximum (Carnot) efficiency with which the person can perform work? b) If the person could work with that efficiency, at what rate, in watts, would he or she have to shed waste heat to the surroundings? c) With a skin area of \(1.50 \mathrm{~m}^{2},\) a skin temperature of \(27.0^{\circ} \mathrm{C}\), and an effective emissivity of \(e=0.600,\) at what net rate does this person radiate heat to the \(20.0^{\circ} \mathrm{C}\) surroundings? d) The rest of the waste heat must be removed by evaporating water, either as perspiration or from the lungs. At body temperature, the latent heat of vaporization of water is \(575 \mathrm{cal} / \mathrm{g}\). At what rate, in grams per hour, does this person lose water? e) Estimate the rate at which the person gains entropy. Assume that all the required evaporation of water takes place in the lungs, at the core body temperature of \(37.0^{\circ} \mathrm{C}\)
A heat engine cycle often used in refrigeration, is the Brayton cycle, which involves an adiabatic compression, followed by an isobaric expansion, an adiabatic expansion, and finally an isobaric compression. The system begins at temperature \(T_{1}\) and transitions to temperatures \(T_{2}, T_{3},\) and \(T_{4}\) after respective parts of the cycle. a) Sketch this cycle on a \(p V\) -diagram. b) Show that the efficiency of the overall cycle is given by \(\epsilon=1-\left(T_{4}-T_{1}\right) /\left(T_{3}-T_{2}\right)\).
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