Question

A glass window is exactly 19 cm by 25 cm at 6°C. By how much has its area increased when its temperature is 31°C, assuming that it can expand freely? cm2

Answer 1

Answer :

First find the original area:
A = (19 cm)(25 cm) = 475 cm²

The elongation of a material due to thermal expansion is given by:

δ = αΔTL

δ = elongation
α = coefficient of thermal expansion = 9 x 10^-6 /°C
ΔT = change in temperature = 31°C - 6°C = 25°C
L = length

Find the elongation in each direction:

δx = (9 x 10^-6 /°C)(25°C)(19 cm) = 0.004275 cm
δy = (9 x 10^-6 /°C)(25°C)(25 cm) = 0.005625 cm

Now add those to the original lengths, and find the new area:
(19.004275 cm)(25.005625 cm) ≈ 475.213 cm²

So the area has increased by 0.213 cm², or about 0.05%.