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A pair of eye glass frames is made of epoxy plastic at room temperature 20.0°c, the frames have circular lens holes 2.20cm in radius. To what temperature must the frame be heated if lens 2.21cm in radius are to be inserted in them? The average coefficient of linear expansion for epoxyis 1.30x10-4°c-1.

A pair of eye glass frames is made of epoxy plastic at room temperature 20.0°c, the frames have circular lens holes 2.20cm in radius. To what temperature must the frame be heated if lens 2.21cm in radius are to be inserted in them? The average coefficient of linear expansion for epoxyis 1.30x10-4°c-1.

Grade:12th pass

1 Answers

Arun
25758 Points
4 years ago
Recall that, by linear expansion: 
∆L = aL₁∆T. 

Solving this for ∆T gives: 
∆T = ∆L/(aL₁) 

Since the want the lenses to be 2.21 cm and they are initially 2.20 cm, we have: 
∆L = 2.21 - 2.20 = 0.01 cm. 

Plugging this into our equation gives: 
∆T = ∆L/(aL₁) 
= (0.01 cm)/[(1.30 x 10^-4° C^-1)(2.20 cm)] 
= 34.9°C. 

Therefore, the temperature desired is 20.0 + 34.9 = 54.9°C. 

I hope this helps!

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