Homework 1-solutions

# Homework 1-solutions - poincy(cp26467 – Homework 1 –...

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Unformatted text preview: poincy (cp26467) – Homework 1 – williams – (999949) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points At what Fahrenheit temperature are the Cel- sius and Fahrenheit temperatures numerically equal? Correct answer:- 40 ◦ F. Explanation: T F = 9 5 T C + 32 , so x = 9 5 x + 32- 4 5 x = 32 x =- 5 4 (32) =- 40 , so- 40 ◦ C =- 40 ◦ F. 002 10.0 points The temperature of a 2 . 6 m copper pipe is raised from 72 ◦ C to 977 ◦ C. What is its change in length? Assume the coefficient of linear expansion for copper is 1 . 7 × 10 − 5 ( ◦ C) − 1 . Correct answer: 0 . 040001 m. Explanation: Given : L 1 = 2 . 6 m , T 1 = 72 ◦ C , T 2 = 977 ◦ C , and α = 1 . 7 × 10 − 5 ( ◦ C) − 1 . The change in length is given by Δ L = αL 1 Δ T = αL 1 ( T 2- T 1 ) = bracketleftbig 1 . 7 × 10 − 5 ( ◦ C) − 1 bracketrightbig (2 . 6 m) × (977 ◦ C- 72 ◦ C) = . 040001 m 003 10.0 points A gold ring has an inner diameter of 0 . 9754 cm at a temperature of 10 ◦ C. Determine its inner diameter at 120 ◦ C. (The coefficient of linear expansion is 1 . 42 × 10 − 5 ( ◦ C) − 1 .) Correct answer: 0 . 976924 cm. Explanation: Given : L 1 = 0 . 9754 cm , T 1 = 10 ◦ C , T 2 = 120 ◦ C , and α = 1 . 42 × 10 − 5 ( ◦ C) − 1 . The diameter expands by Δ L = αL 1 Δ T = αL 1 ( T 2- T 1 ) = bracketleftbig 1 . 42 × 10 − 5 ( ◦ C) − 1 bracketrightbig × (0 . 9754 cm) (120 ◦ C- 10 ◦ C) = 0 . 00152357 cm . and L 2 = L 1 + Δ L = 0 . 9754 cm + 0 . 00152357 cm = . 976924 cm . 004 10.0 points A square hole 6 . 1 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 74 K. The coefficient of expasion is 1 . 7 × 10 − 5 ( ◦ C) − 1 . Correct answer: 0 . 0936204 cm 2 . Explanation: Let : L = 6 . 1 cm , Δ T = 74 K , and α = 1 . 7 × 10 − 5 ( ◦ C) − 1 . poincy (cp26467) – Homework 1 – williams – (999949) 2 Each side of the hole expands linearly by Δ L = Lα Δ T , so the area expands by Δ A = ( L + Δ L ) 2- A . Since Δ L is much smaller than L we should keep only the linear term in Δ L , so Δ A = 2 L Δ L = 2 αA Δ T = 2 αL 2 Δ T = 2 bracketleftbig 1 . 7 × 10 − 5 ( ◦ C) − 1 bracketrightbig ( 37 . 21 cm 2 ) (74 K) = . 0936204 cm 2 . 005 10.0 points A lake contains approximately 1 . 24 × 10 6 kg of water. What is its heat capacity? The specific heat of water is 1000 cal / kg · ◦ C....
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## This note was uploaded on 03/14/2011 for the course PHY 2049 taught by Professor Williams during the Spring '11 term at Florida A&M.

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Homework 1-solutions - poincy(cp26467 – Homework 1 –...

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