First slide

Thermal expansion

Question

A surveyor’s 30 m steel tape is correct at a temperature of 20°C. The distance between two points, as measured by this tape on a day when the temperature is 35°C, is 26 m. What is the true distance between the points? $(α_{steel} = 1 .2 \times 10^{- 5} /^{\circ} C)$

Easy

Solution

Let temperature above the correct temperature be
$\Rightarrow θ = 35 - 20 = 15^{\circ} C$ (Using the relation)
Correct length = measured length $(1 + αθ)$
True distance between the points = 26(1+ 1.2 x10^-5 X1.5)
$\Rightarrow True distance = 26 .00476 m$

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