The frames for a pair of eyeglasses have a radius of 2.14 cm at 20.0°C. Lenses with radius of 2.16 cm have to be inserted into these frames. To what temperature must the technician heat the frames to accommodate the lenses? The frames are made of a material whose thermal expansion coefficient is 1.30 10-4/°C.

The technician must heat the frame to a temperature of T₂ = 0.0072°C

Explanation:

Change in one-dimension of an object upon heating is given by the following equation:

ΔL = α L ΔT

For the radius this equation can be re-written as follows:

ΔR = α R ΔT

where,

ΔR = Change in Radius = 2.16 cm - 2.14 cm = 0.02 cm

α = Thermal Expansion Coefficient = 1.3 x 10⁻⁴ / °C

R = Original Radius = 2.14 cm

ΔT = Change in Temperature = T₂ - 20°C

Therefore,

0.02 cm = (1.3 x 10⁻⁴ / °C) (2.14 cm) (T₂ - 20°C)

T₂ - 20°C = (0.02 cm) / (1.3 x 10⁻⁴ / °C) (2.14 cm)

T₂ = 0.0072°C + 20°C

T₂ = 20.0072°C