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The relationship Lf = Li(1 + α ΔT ) is an approximation that works when the average coefficient of expansion is small. If α is large, one must integrate the relationship dL/dT = α L to determine the final length.

a)Assuming that the average coefficient of linear expansion is constant as L varies, determine a general expression for the final length. Use L_i for Li, alpha for α, and DeltaT for ΔT as necessary.

b)Given a rod of length 4.00 m and a temperature change of 100.0°C, determine the error caused by the approximation when α = 2.00 multiplied by 10-5 (°C)-1 (a typical value for a metal)

2.

Lf = Li(1 + α ΔT )

α(Li)(ΔT)

3.

b)

( 4( 1 + (2.00E-5(100)) ) / (4*100*2.00E-5)

.002/1.002 = .001996008 * 100 = .1996008

It says that:

Your answer is off by a multiple of ten.% for part b

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# Homework Help: Determine error caused by average coefficient of expansion approximation.

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