Question

A rectangular plate has an area of 19 cm². If the temperature increases by 150 ◦C, calculate the increase in the area. Use 4 × 10⁻⁶ (◦C)−1 as an average coefficient of linear expansion, and ignore terms of second order. Answer in units of cm²

Answer 1

Using the formula for thermal expansion in two dimensions, the increase in area of a rectangular plate with an original area of 19 cm² subject to a temperature increase of 150 °C is calculated to be 0.0228 cm².

Step-by-step explanation:

When considering the effects of thermal expansion in two dimensions, we can find the increase in area due to a change in temperature using the formula ΔA = 2αAΔT. In this particular case, we're given an original area (A) of 19 cm², a temperature increase (ΔT) of 150 °C, and a coefficient of linear expansion (α) of 4 × 10⁻⁶ (°C)⁻¹.

To calculate the increase in area, we'll substitute the known values into the formula:

ΔA = 2 × (4 × 10⁻⁶) × 19 cm² × 150 °C

After performing the multiplication, we find that:

ΔA = 2 × (4 × 10⁻⁶) × 19 × 150

ΔA = 2 × 76 × 10⁻⁶ × 150

ΔA = 0.0228 cm²

Therefore, the increase in the area of the rectangular plate due to the temperature increase is 0.0228 cm².