Chapter 20: Problem 21
You are given a beaker of water. What can you do to increase its entropy? What can you do to decrease its entropy?
Chapter 20: Problem 21
You are given a beaker of water. What can you do to increase its entropy? What can you do to decrease its entropy?
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Get started for freeSuppose 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 they 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 \(37.0^{\circ} \mathrm{C}\).
What is the minimum amount of work that must be done to extract \(500.0 \mathrm{~J}\) of heat from a massive object at a temperature of \(27.0^{\circ} \mathrm{C}\) while releasing heat to a high temperature reservoir with a temperature of \(100.0^{\circ} \mathrm{C} ?\)
An outboard motor for a boat is cooled by lake water at \(15.0^{\circ} \mathrm{C}\) and has a compression ratio of \(10.0 .\) Assume that the air is a diatomic gas. a) Calculate the efficiency of the engine's Otto cycle. b) Using your answer to part (a) and the fact that the efficiency of the Carnot cycle is greater than that of the Otto cycle, estimate the maximum temperature of the engine.
A key feature of thermodynamics is the fact that the internal energy, \(E_{\text {int }}\) of a system and its entropy, \(S\), are state variables; that is, they depend only on the thermodynamic state of the system and not on the processes by which it reached that state (unlike, for example, the heat content, \(Q\) ). This means that the differentials \(d E_{\text {int }}=T d S-p d V\) and \(d S=\) \(T^{-1} d E_{\text {int }}+p T^{-1} d V,\) where \(T\) is temperature (in kelvins), \(p\) is pressure, and \(V\) is volume, are exact differentials as defined in calculus. What relationships follow from this fact?
1 .00 mole of a monatomic ideal gas at a pressure of 4.00 atm and a volume of \(30.0 \mathrm{~L}\) is isothermically expanded to a pressure of 1.00 atm and a volume of \(120.0 \mathrm{~L}\). Next, it is compressed at a constant pressure until its volume is \(30.0 \mathrm{~L}\), and then its pressure is increased at the constant volume of \(30.0 \mathrm{~L}\). What is the efficiency of this heat engine cycle?
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