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The difference between lenghts of a cert...

The difference between lenghts of a certain brass rod and of a steel rod is claimed to be constant at all temperatures. Is this possible?

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If `L_(B)` and `L_(S)` are the lengths of brass and steel rods respectively at a given temperature, then the lenghts of the rods when temperature is changed by `theta .^(@)C`.
` L'_(B)=L_(B)(1+alpha_(B) Deltatheta )` and `L'_(S)= L_(S)(1+alpha_(B)Deltatheta)`. So that `L'_(B) - L'_(S) = L_(B) -L_(S) + (L_(B)alpha_(B) -L_(S)alpha_(S))Deltatheta`
So ` (L'_(B)- L'_(S))` will be equal to `(L_(B) -L_(S))` at all temperature if , ` L_(B)alpha_(B) - L_(S)alpha_(S) = 0` [as` Delta theta ne 0]` or `(L_(B))/ (L_(S)) = (alpha_(S))/(alpha_(B))`
i.e., the difference in the lengths of the two rods will be independent of temperature if the lengths are in the
inverse ratio of their coefficients of linear expansion.
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