Question

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.

Answer 1

To fit lenses into the eyeglass frames by the specified radius, the technician should heat the frames to approximately 92.9°C.

Step-by-step explanation:

The student's question pertains to the thermal expansion of materials, specifically the expansion of eyeglass frames to fit lenses. To answer the question, the linear thermal expansion formula can be used: ΔL = αL₀ΔT, where ΔL is the change in length, α is the coefficient of thermal expansion, L₀ is the original length, and ΔT is the change in temperature.

To find the temperature the frames must be heated to, you first calculate the needed expansion: ΔL = 2.16 cm - 2.14 cm = 0.02 cm. Then you solve for ΔT:

ΝeltaT = ΔL / (α * L₀) = 0.02 cm / (1.30 * 10^-4/°C * 2.14 cm) = ΔT = approximately 72.9 °C.

Since the original temperature is 20.0°C, the new temperature T = 20.0°C + ΔT = 20.0°C + 72.9°C = 92.9°C (rounded to one decimal place).

Hence, the technician should heat the frames to 92.9°C to accommodate the lenses.