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Homework 9 Solution

# Homework 9 Solution - Version PREVIEW Homework 9...

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Version PREVIEW – Homework 9 – Savrasov – (39825) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Expanding Gas 03 001 10.0 points A sample of ideal gas is expanded to twice its original volume of 0 . 4 m 3 in a quasi-static process for which P = α V 2 with α = 4 atm / m 6 , V a = 0 . 4 m 3 and V b = 0 . 8 m 3 , as shown in the figure. V P P = ( 4 a t m / m 6 ) V 2 0 . 4 m 3 0 . 8 m 3 How much work was done by the expanding gas? Correct answer: 60509 . 9 J. Explanation: Given : α = 4 atm / m 6 , V a = 0 . 4 m 3 , and V b = 0 . 8 m 3 . The work done by the gas is the area under the curve P = α V 2 between V a and V b : W ab = integraldisplay b a P d V = integraldisplay b a α V 2 d V = α ( V 3 b - V 3 a ) 3 = (4 atm / m 6 ) bracketleftbig (0 . 8 m 3 ) 3 - (0 . 4 m 3 ) 3 bracketrightbig 3 = 60509 . 9 J . Gas Expands Isothermally 002 10.0 points Given: R = 8 . 31 J / K · mol . 1 mol of an ideal gas expands isothermally at 373 K to 2 . 3 its initial volume. Find the heat flow into the system. Correct answer: 2581 . 71 J. Explanation: Given : n = 1 mol , R = 8 . 31 J / K · mol , T = 373 K , and V f = 2 . 3 V i . This is an isothermal process, so the inter- nal energy of the ideal gas is constant. Thus the heat flowing into the system is equal to the work done to the system: W = n R T ln parenleftbigg V f V i parenrightbigg = (1 mol) (8 . 31 J / K · mol) (373 K) × ln (2 . 3) = 2581 . 71 J .

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Homework 9 Solution - Version PREVIEW Homework 9...

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