An aluminum-alloy rod has a length of 10.007 cm at 16.600 °C and a length of 10.

Question

An aluminum-alloy rod has a length of 10.007 cm at 16.600 °C and a length of 10.023 cm at the boiling point of water.

a.)What is the length of the rod at the freezing point of water? (Answer to the nearest 0.001 cm.)

b.)What is the temperature if the length of the rod is 10.020 cm?

Explanation / Answer

a). change in length = original length *coefficient of linear expansion*change in temperature => 10.007 -10.023 = 10.023 *coefficient of linear expansion* (16.6 -100) => coefficient of linear expansion = 1.914 *10^-5 per degree celsius L' at 0 degree celsius = L*[1+coefficient of linear expansion*change in temperature] => L' = 10.023 *[1+1.914*10^-5 *(0-100)] => L' = 10.004 cm b). L' = L*[1+coefficient of linear expansion*change in temperature] =>10.02 = 10.023 *[1+1.914*10^-5* (T -100)] => T = 84.362 degree celsius

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