Explanation Given: The length of thin silver wire L = 18 cm The temperature T = 30 ° C Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: The length of thin silver wire L = 18 cm The temperature T = 30 ° C We have to find the length when T = 25 ° C if the coefficient of thermal expansion is k = 1.9 × 10 − 5 ° C − 1 . The change in length Δ L when T decreases from 30 ° C to 25 ° C , that is Δ T = − 5 ° . Consider the equation, when change of length with respect to temperature. d L d T = k L Substitute 1.9 × 10 − 5 for k and 18 for L in the above equation

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 4.1, Problem 37E

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Find the value of ΔL when T decreases to 25°C if the coefficient of thermal expansion is k=1.9×10−5°C−1.

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Chapter 4.1, Problem 36E

Chapter 4.1, Problem 38E

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Find the value of Δ L when T decreases to 25 ° C if the coefficient of thermal expansion is k = 1.9 × 10 − 5 ° C − 1 .

Solution Summary: The author calculates the value of Delta L when T decreases to 25°C if the coefficient of thermal expansion is

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Find the value of ΔL when T decreases to 25°C if the coefficient of thermal expansion is k=1.9×10−5°C−1.

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Chapter 4 Solutions