An aluminum-alloy rod has a length of 10.010 cm at 17.600 degree C and a length

Question

An aluminum-alloy rod has a length of 10.010 cm at 17.600 degree C and a length of 10.018 cm at the boiling point of water. What is the length of the rod at the freezing point of water? (Answer to the nearest 0.001 cm.) What is the temperature if the length of the rod is 10.015 cm? Did you calculate the coefficient of linear expansion by using the given lengths at the given temperatures? Once the coefficient is known, can you find (a) the change in length when the temperature is changed to the freezing point? (b) Do you see that you are being indirectly told the change in length?

Explanation / Answer

Length change = Original length x alpha x delta T alpha aluminum = 24 10^-6 °C alpha steel = 13 10^-6 °C Aluminium ?L = L° a ?t = 1.2 * 24 10^-6 * 20 = 0.000576 cm Steel-------?L = L° a ?t = 2 * 13 10^-6 * 20 = 0.00052 cm ?L road = 0.000576 + 0.00052 = 0.001096 cm = 1.096 10^-3 c

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