A thin brass sheet at 100C and a thin steel sheet at 200C have the same surface area. The common temperature (in 0C ) at which both would have the same area is given by -k40C. Then the value of k is___(Given coefficient of linear expansion for brass and steel are 19×10−6 0C−1 and 11×10−6 0C−1 respectively).

[A1]=[A2] A1[1+β1(t−10)]=A2[1+β2(t−20)]⇒8t=−30;t=-1540C ∴ k=15

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A thin brass sheet at $10^{0} C$ and a thin steel sheet at $20^{0} C$ have the same surface area. The common temperature (in $^{0} C$ ) at which both would have the same area is given by ${\frac{- k}{4}}^{0} C$ . Then the value of $k$ is___
(Given coefficient of linear expansion for brass and steel are $19 \times 10^{- 6}^{0} C^{- 1}$ and $11 \times 10^{- 6}^{0} C^{- 1}$ respectively).

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answer is 15.

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$[A_{1}] = {[A_{2}]}_{}$

$A_{1} [1 + β_{1} (t - 10)] = A_{2} [1 + β_{2} (t - 20)]$

$\Rightarrow 8 t = - 30; t = {\frac{- 15}{4}}^{0} C ∴ k = 15$

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