A pair of eyeglass frames are made of an epoxy plastic (coefficient of linear expansion = 1.30 ✕ 10-4°C-1). At room temperature (20.0°C), the frames have circular lens holes 2.34 cm in radius. To what temperature must the frames be heated if lenses 2.35 cm in radius are to be inserted into them? °C

Final temperature = 52.44 °C

Explanation:

We have equation for thermal expansion

ΔL = LαΔT

We have change in length = Circumference of 2.35 cm radius - Circumference of 2.34 cm radius = 2π x 2.35 - 2π x 2.34 = 0.062 cm

Length of eyeglass frame = 2π x 2.34 = 14.70 cm

Coefficient of linear expansion, α = 1.30 x 10⁻⁴ °C⁻¹

Substituting

0.062 = 14.70 x 1.30 x 10⁻⁴ x ΔT

ΔT = 32.44°C

Final temperature = 32.44 + 20 = 52.44 °C