Hmwk_13_Solutions

Hmwk_13_Solutions - Physics 221 Fall 2008 Homework #13...

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1 Physics 221 Fall 2008 Homework #13 Solutions Ch. 17; Ch. 18:1-3 Due Tues, Dec 2, 2008 13.1 The boiling point of liquid nitrogen (N 2 ) is 77 K. What is this temperature in ˚C? In ˚F? T C = T K ± 273.15 = 77 ± 273.15 = ± 196 ˚C . T F = (9/5) T C + 32 = (9/5)( ± 196) + 32 = ± 321 ˚F . 13.2 Here is how to fit a square peg into a round hole. At 20 ˚C, a square steel peg is 2.0000 cm on a side, and a round hole in an aluminum plate has a diameter of 2.8200 cm. The linear thermal expansion coefficient of aluminum is 2.4 ² 10 ± 5 /˚C. (a) Show that the square peg initially will not fit into the round hole. The diameter of the circle that encircles the square peg (the distance across the diagonal) is d = 2 L = 2 ( 2 . 0000 cm) = 2 . 8284 cm . This diameter is greater than the diameter of the round hole, so the square peg will not fit into the hole. (b) Explain why the diameter of the hole in the aluminum plate will increase, rather than decrease, if the temperature of the aluminum plate is increased. What temperature must the aluminum plate be increased to in order that the square peg will fit into the round hole? The distance between each pair of atoms increases when the plate is heated, including the distance between the atoms around the circumference of the hole. Therefore when the plate is heated the circumference of the hole increases, and therefore so does the diameter of the hole. For the hole diameter d h , it needs to increase by an amount ³ d h = 0.0084 cm. We have ³ d h = ´ d h0 ³ T . Therefore, ± T = ± d h ² d h0 = 0 . 0084 cm (2.4 ³ 10 -5 / °C)(2.8200 cm) = 124 °C . T final = T initial + ³ T = 20 ˚C + 124 ˚C = 144 ˚C . (c) If the square peg is put into the round hole in the hot aluminum plate, and the aluminum plate cooled back to 20 ˚C, what do you think will happen?
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This note was uploaded on 01/28/2010 for the course PHYSICS 221 taught by Professor Johnson during the Fall '06 term at Iowa State.

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Hmwk_13_Solutions - Physics 221 Fall 2008 Homework #13...

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