Question

A square plate of side 10cm is made of a metal of linear expansivity 2 X 10^−5/K. As the plate is heated from 30°C to 100°C, the area of one face of the plate will increase to__________

Answer 1

Let: $L = 10$ (cm)

$\alpha = 2 \times 10^{-5}$

$t1 = 30{}^{\circ}C$

$t2 = 100{}^{\circ}C$

At heating the plate linearly extends equally in two dimensions:

$\Delta S = \Delta L^{2}$

Side of plate will increase to:

$\Delta L = L \times \alpha (t2 - t1)$

$\Delta L = 10 \times 2 \times 10^{-5} \times (100 - 30) = 0.014 \, (\text{cm})$

Area of one face of the plate will increase to:

$\Delta S = 0.014^{2} = 0.000196 \, (\text{cm}^{2})$