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HW10solution08

# HW10solution08 - Version PREVIEW HW 10(solution is...

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Version PREVIEW – HW 10 (solution is available) – Savrasov – (39824) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Serway CP 12 33 001 10.0 points A nuclear power plant has an electrical power output of 1333 MW and operates with an efficiency of 33%. If excess energy is carried away from the plant by a river with a flow rate of 1 × 10 6 kg / s, what is the rise in temperature of the flowing water? Correct answer: 0 . 646535 C. Explanation: Given : P output = 1333 MW = 1 . 333 × 10 9 W , e = 0 . 33 , and Δ m Δ t = 1 × 10 6 kg / s . The Carnot efficiency is e = W Q h and P = W t = e c Q h t Q h = P t e . From e = Q h - Q c Q h , the energy expelled in time t is Q c = Q h (1 - e ) = P t e (1 - e ) = P t parenleftbigg 1 e - 1 parenrightbigg . In time t , the mass of cooling water used is m = Δ m Δ t · t , so its rise in temperature is Δ T = Q c m c = P t Δ m Δ t t c parenleftbigg 1 e - 1 parenrightbigg = P Δ m Δ t c parenleftbigg 1 e - 1 parenrightbigg = 1 . 333 × 10 9 W (1 × 10 6 kg / s) (4186 J / kg · C) × parenleftbigg 1 0 . 33 - 1 parenrightbigg = 0 . 646535 C . Temperature Increase 002 10.0 points The efficiency of a 1232 MW nuclear power plant is 38 . 4%.

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