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Assignment 5 Solution

# Assignment 5 Solution - PHYS-232 Heat and Waves Homework 5...

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PHYS-232 Heat and Waves - Homework 5 Winter Semester 2008 Due on Thursday, January 31, 2008 1. C Al = 0 . 887 Jg 1 K 1 . The heat loss from Al is: Δ Q A = C Al m A Δ T = 0 . 887 · 5 · (40 - 22) = 79 . 83 J , which is the heat transferred to water in A: Δ Q A = C H 2 O m H 2 O Δ T H 2 O = 4 . 184 · m H 2 O · (22 - 20). m H 2 O = 9 . 54 g . The energy gain for water in B is: Δ Q B = 9 . 54 · (4 . 184) · (21 . 5 - 20 . 5) = 59 . 87 J . Δ Q B = 5 · C alloy · (40 - 21 . 5), so C alloy = 0 . 6473 Jg 1 K 1 . 2. (a) The mercury thermometer from my medicine cabinet has a roughly cylin- drical bulb that measures 4 mm in diameter by 5 mm long. Its volume is there- fore about 60 mm 3 . Under a 1 C temperature increase, the volume of the mer- cury should increase by: Δ V = β · V · Δ T = (1 . 81 × 10 4 K 1 )(60 mm 3 )(1 K ) = 0 . 011 mm 3 . The expansion takes place inside a narrow tube with a length of 8 . 5 mm and unknown cross-sectional area. Assuming that the tube is cylin- drical, its radius would have to be r = radicalBig Δ V/πl = radicalBig 0 . 11 mm 3 (8 . 5 mm ) = 0 . 02 mm , so its diameter would be only 0 . 04 mm .
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