Question

A rectangular steel plate with dimensions of 40.0 cm × 30.0 cm is heated from 14.0°C to 164.0°C. What is its change in area? (Coefficient of linear expansion for steel is 11 × 10−6/C°.)

Answer 1

Answer:

1.98 × 10⁻⁴ meter²

Step-by-step explanation:

A rectangular steel plate having dimensions of 40.0 cm × 30.0 cm is heated from 14.0°C to 164°C.

We have to find the change in its area.

Since formula of Area thermal expansion is

$\propto _{A}=\frac{1}{A}\times \frac{\triangle A}{\triangle T}(\propto _{A}=11\times 10^{-6}perC^{\circ})$

Where $\propto _{A}$ = Area thermal expansion coefficient.

            A = Area of the object

            ΔA = change in area

            ΔT = change in temperature.

By replacing the values in the formula.

11 × 10⁻⁶ = $\frac{1}{(0.40)\times (0.30)}\times \frac{\triangle A}{164-14}$

$11\times 10^{-6}=\frac{1}{12\times 10^{-2}}\times \frac{\triangle A}{150}$

$\triangle A=(11\times 10^{-6}\times 12\times 10^{-2}\times 150)$

= 132 × 150 × 10⁻⁸

= 19800 × 10⁻⁸

= 1.98 × 10⁻⁴ meter²