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 2.27 cm in radius. To what temperature must the frames be heated if lenses 2.28 cm in radius are to be inserted into them?

Answer 1

L1= 2• π• r =2• π • 2.27•10^-2 = 0.1426 m
L2 = 2• π• R =2• π • 2.28•10^-2 = 0.1433 m
ΔL = 6.566•10^-4 m
α = (ΔL/L)/ ΔT,
ΔT=(ΔL/L)/ α = (6.566•10^-4/0.1426)/1.3•10^-4 =35.42oC
T = T(o) + ΔT =20 +35.42 = 55.42 oC