Question #129906

A metal rod of length 15 cm is heated to 38 °C. If the length of rod expands to 15.12 cm after some time, calculate the coefficient of linear expansion (Room temperature is 27 °C).

Expert's answer

Thermal expansion of the rod is described with the equation: "l_1=l_0(1+\u03b1 \\cdot \u0394T)", where "l_0" is initial length and "l_1" is length after heating/cooling, ΔT is difference of temperatures, α is the coefficient of linear expansion. In our case:

"15.12 \\cdot 10^{-2}=15 \\cdot 10^{-2} \\cdot (1+\u03b1\\cdot (38-27)) \\Rightarrow 15.12=15+\u03b1 \\cdot 11 \\cdot15 \\Rightarrow \u03b1=\\frac {0,12}{11\\cdot15}=7.3\\cdot 10^{-4} \\frac{1}{\u00b0C}"

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