First slide

Thermal expansion

Question

A thin brass sheet at 20°C and a thin steel sheet at 30°C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are respectively, 19 × 10^–6/°C are 11 × 10^–6/°C)

Moderate

A

–6.25°C
B

+6.25°C
C

–3.25°C
D

+3.25°C

Solution

$\begin{array}{l} {(A_{2})}_{brass} = {(A_{2})}_{steel} \\ {(A_{1})}_{br} [1 + b_{Br} (t - 20)] = {(A_{1})}_{st} [1 + b_{St} (t - 30)] \end{array}$
$Given {(A_{1})}_{br} = {(A_{1})}_{st}$

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