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Question
The length of a ceramic block is being measured by a metallic ruler, which gives readings L1 at temperature T1, and L2 at a temperature T2. It is known that the ruler gives a correct reading at temperature T, and that the ceramic block does not significantly expand for the temperature differences in question. What is the coefficient of linear expansion of the ruler?
The length of a ceramic block is being measured by a metallic ruler, which gives readings L1 at temperature T1, and L2 at a temperature T2. It is known that the ruler gives a correct reading at temperature T, and that the ceramic block does not significantly expand for the temperature differences in question. What is the coefficient of linear expansion of the ruler?
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Solution
The correct option is A (L2−L1T(L2−L1)+L1T1−L2T2)
It is given in the question, that the scale gives a correct reading at temperature T. Calling the correct length L, we can write the following relations.
L1[1+α(T1−T)] = L2[1+α(T2−T)]
⇒ = α[L1(T1−T)−L2(T2−T)] = L2−L1
⇒ α = [L2−L1T(L2−L1)+L1T1−L2T2]
(L2−L1T(L2−L1)+L1T1−L2T2)
It is given in the question, that the scale gives a correct reading at temperature T. Calling the correct length L, we can write the following relations.
L1[1+α(T1−T)] = L2[1+α(T2−T)]
⇒ = α[L1(T1−T)−L2(T2−T)] = L2−L1
⇒ α = [L2−L1T(L2−L1)+L1T1−L2T2]
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