Solving for Temp Change of Epoxy Frames for Lenses Insertion

In summary, the problem is asking for the temperature at which a pair of eyeglass frames made of epoxy plastic must be heated in order for lenses with a slightly larger radius to fit. The average coefficient of linear expansion for epoxy is provided and the relationship between temperature and length change is explained. The units for the coefficient are in °C^-1 or K^-1 depending on the choice of temperature unit.
  • #1
11
1

Homework Statement


This is the problem.

A pair of eyeglass frames is made of epoxy plastic. At
room temperature (20.0°C), the frames have circular
lens holes 2.20 cm in radius. To what temperature must
the frames be heated if lenses 2.21 cm in radius are to
be inserted in them? The average coefficient of linear
expansion for epoxy is 1.30 x 10^-4 (°C)^-1.

Homework Equations

The Attempt at a Solution


I know how to solve this but I'm not very sure what the ℃ elevated to -1 means. Can someone explain what that means and why it is expressed this way?
 
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  • #2
KristinaMr said:

Homework Statement


This is the problem.

A pair of eyeglass frames is made of epoxy plastic. At
room temperature (20.0°C), the frames have circular
lens holes 2.20 cm in radius. To what temperature must
the frames be heated if lenses 2.21 cm in radius are to
be inserted in them? The average coefficient of linear
expansion for epoxy is 1.30 x 10^-4 (°C)^-1.

Homework Equations

The Attempt at a Solution


I know how to solve this but I'm not very sure what the ℃ elevated to -1 means. Can someone explain what that means and why it is expressed this way?
Look at wiki page, "Thermal expansion coefficients for various materials" section. It's just the inverse of the temperature unit.

Write down the equation of the thermal expansion, and weigh down the units for the thermal coefficient.
 
  • #3
α=(∆L/L)/T

So the units are ℃^-1 because the temperature in the equation is in the denominator (which means T ^-1) . Right?
 
  • #4
KristinaMr said:
α=(∆L/L)/T

So the units are ℃^-1 because the temperature in the equation is in the denominator (which means T ^-1) . Right?

Yes. The physical unit for the length is irrelevant because you have (( ΔL/L )) which always cancels out.

The choice of the unit for the temperature influence the unit of your coefficient and vice versa. You can choose to use K (Kelvin) instead of °C (Celsius). In this scenario, α have a unit of K^-1
 
  • #5
Thank you for your help :)
 

1. What is the purpose of solving for temperature change of epoxy frames for lens insertion?

The purpose of solving for temperature change of epoxy frames for lens insertion is to determine the optimal temperature at which the epoxy frames should be heated in order to ensure proper and secure insertion of lenses. This is important because temperature can affect the viscosity and flow of the epoxy, which can impact the bonding and strength of the frames.

2. How do you calculate the temperature change of epoxy frames?

The temperature change of epoxy frames can be calculated by using the formula: ΔT = Q/mc, where ΔT is the temperature change, Q is the heat input, m is the mass of the epoxy, and c is the specific heat capacity of the epoxy.

3. What factors can affect the temperature change of epoxy frames?

There are several factors that can affect the temperature change of epoxy frames, including the type and amount of epoxy used, the initial and desired temperature, the size and shape of the frames, and the heating method. Other external factors such as humidity and air flow can also impact the temperature change.

4. How can temperature change affect the final product of the epoxy frames?

The temperature change can significantly affect the final product of the epoxy frames. If the frames are heated too much or too little, it can result in improper bonding and weak frames. This can lead to lens detachment or breakage, which can be costly and time-consuming to fix.

5. Are there any safety precautions to consider when solving for temperature change of epoxy frames?

Yes, there are some safety precautions to consider when solving for temperature change of epoxy frames. It is important to wear protective gear such as gloves and goggles when handling hot epoxy. It is also recommended to work in a well-ventilated area and to follow the manufacturer's instructions for heating the epoxy. Additionally, it is important to properly dispose of any excess epoxy and to clean up any spills immediately.

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