Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 13, Problem 6P
To determine

Rank the increase in length from greatest to smallest.

Expert Solution & Answer
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Answer to Problem 6P

The rank of the increase in length from greatest to smallest is (b)=(d)=(e),(a),(c).

Explanation of Solution

Write an expression for the increase in length.

ΔL=LαΔT=Lα(TfTi) (I)

Here, ΔL is the increase in length, L is the initial length, α is the coefficient of thermal expansion, ΔT is the change in temperature, Tf is final temperature and Ti is the initial temperature.

Conclusion:

Consider slab (a).

Substitute 90cm for L, 40°C for Tf, 20°C for Ti and 8×106K1 for α in equation (I) to find ΔL.

ΔL=((90cm)(1m102cm))(8×106K1)((40°C+273.15K/°C)(20°C+273.15K/°C))=(0.90m)(8×106K1)(20K)=1.44×104m

Consider slab (b).

Substitute 90cm for L, 50°C for Tf, 20°C for Ti and 8×106K1 for α in equation (I) to find ΔL.

ΔL=((90cm)(1m102cm))(8×106K1)((50°C+273.15K/°C)(20°C+273.15K/°C))=(0.90m)(8×106K1)(30K)=2.16×104m

Consider slab (c).

Substitute 60cm for L, 40°C for Tf, 20°C for Ti and 8×106K1 for α in equation (I) to find ΔL.

ΔL=((60cm)(1m102cm))(8×106K1)((40°C+273.15K/°C)(20°C+273.15K/°C))=(0.60m)(8×106K1)(20K)=0.96×104m

Consider slab (d).

Substitute 90cm for L, 40°C for Tf, 20°C for Ti and 12×106K1 for α in equation (I) to find ΔL.

ΔL=((90cm)(1m102cm))(12×106K1)((40°C+273.15K/°C)(20°C+273.15K/°C))=(0.90m)(12×106K1)(20K)=2.16×104m

Consider slab (e).

Substitute 60cm for L, 50°C for Tf, 20°C for Ti and 12×106K1 for α in equation (I) to find ΔL.

ΔL=((60cm)(1m102cm))(12×106K1)((50°C+273.15K/°C)(20°C+273.15K/°C))=(0.60m)(12×106K1)(30K)=2.16×104m

Thus, the rank of the increase in length from greatest to smallest is (b)=(d)=(e),(a),(c).

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Chapter 13 Solutions

Physics

Ch. 13.6 - Prob. 13.7PPCh. 13.7 - Prob. 13.8PPCh. 13.8 - Prob. 13.9PPCh. 13 - Prob. 1CQCh. 13 - Prob. 2CQCh. 13 - Prob. 3CQCh. 13 - Prob. 4CQCh. 13 - Prob. 5CQCh. 13 - Prob. 6CQCh. 13 - Prob. 7CQCh. 13 - Prob. 8CQCh. 13 - Prob. 9CQCh. 13 - Prob. 10CQCh. 13 - Prob. 11CQCh. 13 - Prob. 12CQCh. 13 - Prob. 13CQCh. 13 - Prob. 14CQCh. 13 - Prob. 15CQCh. 13 - Prob. 16CQCh. 13 - Prob. 17CQCh. 13 - Prob. 18CQCh. 13 - Prob. 19CQCh. 13 - Prob. 20CQCh. 13 - Prob. 1MCQCh. 13 - Prob. 2MCQCh. 13 - Prob. 3MCQCh. 13 - Prob. 4MCQCh. 13 - Prob. 5MCQCh. 13 - Prob. 6MCQCh. 13 - Prob. 7MCQCh. 13 - Prob. 8MCQCh. 13 - Prob. 9MCQCh. 13 - Prob. 10MCQCh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10PCh. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - Prob. 17PCh. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - Prob. 20PCh. 13 - Prob. 21PCh. 13 - 22. A copper washer is to be fit in place over a...Ch. 13 - 23. Repeat Problem 22, but now the copper washer...Ch. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - Prob. 63PCh. 13 - Prob. 64PCh. 13 - Prob. 65PCh. 13 - Prob. 66PCh. 13 - Prob. 67PCh. 13 - Prob. 68PCh. 13 - Prob. 69PCh. 13 - Prob. 70PCh. 13 - Prob. 71PCh. 13 - Prob. 72PCh. 13 - Prob. 73PCh. 13 - Prob. 74PCh. 13 - Prob. 75PCh. 13 - Prob. 76PCh. 13 - Prob. 77PCh. 13 - Prob. 78PCh. 13 - Prob. 79PCh. 13 - Prob. 80PCh. 13 - Prob. 81PCh. 13 - Prob. 82PCh. 13 - Prob. 83PCh. 13 - Prob. 84PCh. 13 - Prob. 85PCh. 13 - Prob. 86PCh. 13 - Prob. 87PCh. 13 - Prob. 88PCh. 13 - Prob. 89PCh. 13 - Prob. 90PCh. 13 - Prob. 91PCh. 13 - Prob. 92PCh. 13 - Prob. 93PCh. 13 - Prob. 94PCh. 13 - Prob. 95PCh. 13 - Prob. 96PCh. 13 - Prob. 97PCh. 13 - Prob. 98PCh. 13 - Prob. 99PCh. 13 - Prob. 100PCh. 13 - Prob. 101PCh. 13 - Prob. 102PCh. 13 - Prob. 103PCh. 13 - Prob. 104PCh. 13 - Prob. 105PCh. 13 - Prob. 106PCh. 13 - Prob. 107PCh. 13 - Prob. 108PCh. 13 - Prob. 109PCh. 13 - Prob. 110PCh. 13 - Prob. 111PCh. 13 - Prob. 112PCh. 13 - 113. A long, narrow steel rod of length 2.5000 m...Ch. 13 - Prob. 114PCh. 13 - Prob. 115PCh. 13 - Prob. 116PCh. 13 - Prob. 117PCh. 13 - Prob. 118PCh. 13 - Prob. 119PCh. 13 - Prob. 120P
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