A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion is 1.30*10^-4 C^-1). At room temperature (20 degrees Celsius, the frames have circular lens holes of 2.20cm in radius. To what temperature must the frames be heated if lenses are 2.21cm in radius are to be inserted into them?
The temperature must be heated to 20.3 degrees Celsius.
To calculate this, use the formula ΔT = (ΔL/L) * α * T, where ΔT is the change in temperature, ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and T is the original temperature.
In this case, ΔL = 0.01 cm, L = 2.20 cm, α = 1.30*10^-4 C^-1, and T = 20 degrees Celsius.
Plugging these values into the formula, we get ΔT = (0.01/2.20) * (1.30*10^-4 C^-1) * 20 = 0.3 degrees Celsius.
Therefore, the temperature must be heated to 20.3 degrees Celsius.