Explanation Given: Initial temperature, T 0 = 15 ° C Initial diameter of the brass plug, l B 0 = 8.755 c m Initial diameter of the iron plug, l I 0 = 8.741 c m Formula used: Δ l = l × α × Δ T , where α is the coefficient of linear expansion of a material Calculation: If we change the temperature, the diameters of the plug and the ring will also change, and this change in diameters will depend on the respective coefficient of linear expansion of the two materials. There will be one temperature, either above or below 15°C, where the two diameters will be equal. The relation between change in length of a substance and change in temperature is given by, Δ l = l i × α × Δ T , where ΔT is the change in temperature andα is the coefficient of linear expansion of a material. The final length is thus given by, l f = l i + Δ l or l f = l i + l i α Δ T = l i ( 1 + α Δ T ) = l i [ 1 + α ( T f – T 0 ) ] For brass, l B f = l B 0 [ 1 + α B ( T f – T 0 ) ] For iron, l I f = l I 0 [ 1 + α I

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ISBN: 9780321625922

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 13, Problem 17P

To determine

The common temperature that both the brass plug and the iron ring have to be brought to for the plug to fit into the ring

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Chapter 13 Solutions

Physics: Principles with Applications

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