hw10 - CHAPTER 22 . - THE SECOND LAW O F THERMODYNAMICS...

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CHAPTER 22 THE SECOND LAW OF .. - -- Problem 3. Estimate the energy that could be extracted by cooling the world's oceans by 1°C. How does your estimate compare with humanity's yearly energy consumption of about 2.5~ lo2' J? Solution The voluine of the oceans is about 1.35~ 1018 m3 (the average depth is 3.73 km over 71% of the earth's surface). The heat extracted by cooling this volume of water by 1°C is Q = pVc AT = (lo3 kg/m3)x (1.35 x 1018 m3)(4184 J/kg.K)(l K) 11 5.65~10~~ J, or about 23,000 times the world's annual energy consumption. THERMODYNAMICS Problem 5. What are the efficiencies of reversible heat engines operating between (a) the normal freezing and boiling points of water, (b) the 25°C temperature at the surface of a tropical ocean and deep water at 4°C' and (c) a 1000°C candle flame and room temperature? Solution The efficiency of a reversible engine, operating between two absolute temperatures, Th > Tc, is given by Equation 22-3. (a) e = 1 - T,/Th = 1 - 273/373 = 26.8%. (b) e = (Th - Tc)/Th = AT/Th = 21/298 = 7.05%. (c) With room temperature at T, = 20°C, e = 98011273 = 77.0%. 9.
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hw10 - CHAPTER 22 . - THE SECOND LAW O F THERMODYNAMICS...

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