W13 HW2 Expansion & Gas Laws-solutions-1

W13 HW2 Expansion & Gas Laws-solutions-1 - chiesa...

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Unformatted text preview: chiesa (dac3234) W13 HW2 Expansion & Gas Laws lacker (Q2 AP) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A steel ball bearing is 7 cm in diameter at 18 C. A bronze plate has a hole that is 6 . 993 cm in diameter at 18 C. What common temperature must they have in order for the ball to just squeeze through the hole? Correct answer: 143 . 298 C. Explanation: Let : d st = 7 cm , T br = 18 C , d br = 6 . 993 cm , T st = 18 C , st = 1 . 1 10 5 ( C) 1 , and br = 1 . 9 10 5 ( C) 1 . Using the law of linear expansion, L new = L (1 + T ) and requiring that the diameters are the same at temperature T , d br [1 + br ( T- T br )] = d st [1 + st ( T- T st )] d br + d br br T- d br br T br = d st + d st st T- d st st T st ( d br br- d st st ) T = d st- d br + d br br T br- d st st T st T = d st- d br d br br- d st st + d br br T br- d st st T st d br br- d st st . Since d br br- d st st = (6 . 993 cm) bracketleftbig 1 . 9 10 5 ( C) 1 bracketrightbig- (7 cm) bracketleftbig 1 . 1 10 5 ( C) 1 bracketrightbig =- 5 . 5867 10 5 cm / C , then T = 7 cm- 6 . 993 cm- 5 . 5867 10 5 cm / C + (6 . 993 cm) bracketleftbig 1 . 9 10 5 ( C) 1 bracketrightbig (18 C)- 5 . 5867 10 5 cm / C- (7 cm) bracketleftbig 1 . 1 10 5 ( C) 1 bracketrightbig (18 C)- 5 . 5867 10 5 cm / C = 143 . 298 C . 002 10.0 points A square hole 12 . 2 cm along each side is cut in a sheet of copper. Find the change in the area of this hole if the temperature of the sheet is increased by 35 K. The coefficient of expasion is 1 . 7 10 5 ( C) 1 . Correct answer: 0 . 17712 cm 2 . Explanation: Let : L = 12 . 2 cm , T = 35 K , and = 1 . 7 10 5 ( C) 1 . Each side of the hole expands linearly by L = L T , so the area expands by A = ( L + L ) 2- A . Since L is much smaller than L we should keep only the linear term in L , so A = 2 L L = 2 A T = 2 L 2 T = 2 bracketleftbig 1 . 7 10 5 ( C) 1 bracketrightbig( 148 . 84 cm 2 ) (35 K) = . 17712 cm 2 ....
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W13 HW2 Expansion & Gas Laws-solutions-1 - chiesa...

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