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Chapter 12: Problem 31
A heat engine operates between a reservoir at \(25^{\circ} \mathrm{C}\) and one at \(375^{\circ} \mathrm{C}\). What is the maximum efficiency possible for this engine?
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Q/C An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of \(8000 \mathrm{~g}\) and an area of \(5.00 \mathrm{~cm}^{2}\) and is free to slide up and down, keeping the pressure of the gas constant. (a) How much work is done on the gas as the temperature of \(0.200\) mol of the gas is raised from \(20.0^{\circ} \mathrm{C}\) to \(300^{\circ} \mathrm{C} ?\) (b) What does the sign of your answer to part (a) indicate?
BIO Hydrothermal vents deep on the ocean floor spout water at temperatures as high as \(570^{\circ} \mathrm{C}\). This temperature is below the boiling point of water because of the immense pressure at that depth. Because the surrounding ocean temperature is at \(4.0^{\circ} \mathrm{C}\), an organism could use the temperature gradient as a source of energy. (a) Assuming the specific heat of water under these conditions is \(1.0 \mathrm{cal} / \mathrm{g}{ }^{\circ}{ }^{\circ} \mathrm{C}\), how much energy is released when \(1.0\) liter of water is cooled from \(570^{\circ} \mathrm{C}\) to \(4.0^{\circ} \mathrm{C}^{\circ}\) (b) What is the maximum usable energy an organism can extract from this energy source? (Assume the organism has some internal type of heat engine acting between the two temperature extremes.) (c) Water from these vents contains hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) at a concentration of \(0.90 \mathrm{mmole} /\) liter. Oxidation of \(1.0\) mole of \(\mathrm{H}_{2} \mathrm{~S}\) produces \(310 \mathrm{~kJ}\) of energy. How much energy is available through \(\mathrm{H}_{2} \mathrm{~S}\) oxidation of 1.0 L of water?
A \(5.0-\mathrm{kg}\) block of aluminum is heated from \(20^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C}\) at atmospheric pressure. Find (a) the work done by the aluminum, (b) the amount of energy transferred to it by heat, and (c) the increase in its internal energy.
A gas is enclosed in a container fitted with a piston of cross-sectional area \(0.150 \mathrm{~m}^{2}\). The pressure of the gas is maintained at \(6000 \mathrm{~Pa}\) as the piston moves inward \(20.0 \mathrm{~cm}\). (a) Calculate the work done by the gas. (b) If the internal energy of the gas decreases by \(8.00 \mathrm{~J}\), find the amount of energy removed from the system by heat during the compression.
Sketch a PV diagram of the following processes: (a) A gas expands at constant pressure \(P_{1}\) from volume \(V_{1}\) to volume \(V_{2}\). It is then kept at constant volume while the pressure is reduced to \(P_{2}\). (b) A gas is reduced in pressure from \(P_{1}\) to \(P_{2}\) while its volume is held constant at \(V_{1}\). It is then expanded at constant pressure \(P_{2}\) to a final volume \(V_{2}\). (c) In which of the processes is more work done by the gas? Why?
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