Answer to Question #245751 in Molecular Physics | Thermodynamics for Cat

Question

A pair of eyeglass frame is made of epoxy plastic. At room temperature of 23.4 oC, the

frames have circular lens 2.3cm in radius.

(a) Show that if the frames are heated to fit the lenses 2.32cm in radius, the temperature

required is given by

𝑇 = 𝑇𝑜 +

1

𝛼 (𝐿𝐿

𝑜 − 1)

With α the coefficient of linear expansivity of epoxy plastic.

(b) The coefficient of epoxy plastic is 1.3 x 10-4 oC-1

Calculate the temperature at which the 2.32cm lenses would be fitted into the frames.

Answer 1

Solution.

$t=23.4^oC;$

$L=2.3\sdot10^{-2}m;$

$L_1=2.32\sdot10^{-2}m;$

$L=L_0(1+\alpha\Delta T)\implies L_0=\dfrac{L}{(1+\alpha\Delta T)};$

$L_0=\dfrac{2.3\sdot10^{-2}}{1+1.3\sdot10^{-4}\sdot3.4}=2.299\sdot10^{-2}m;$

$\Delta T=\dfrac{L1-L_0}{L_0\alpha};$

$\Delta T=\dfrac{2.32\sdot10^{-2}-2.299\sdot10^{-2}}{2.299\sdot10^{-2}\sdot1.3\sdot10^{-4}}=70.26^oC;$

$T=20^oC+70.26^oC=90.26^oC;$

Answer: $90.26^oC.$