Question

At 30°c, the area of a sheet of aluminium is 40cm^2 and the coefficient of linear expansion is 24 × 10^-6. Determine the final temperature if the final area is 40.wcm^2

Answer 1

Answer:

At 30°c, the area of a sheet of aluminum is 40cm^2 and the coefficient of linear expansion is 24 × 10^-6, the final temperature if the final area is 40cm^2 is $19*10^{3}$°C

Explanation:

• The linear expansion is the change in length of an object along one direction (length) with the rise in temperature, that is $\alpha =$ΔL/$L_{0}$ΔT

         $\alpha$-coefficient of linear expansion

• for an Aluminum sheet of initial length, $L_{0}$ the area is $A_{0}$ initially at a temperature $T{_i}$

• now the temperature changed to $T_{f}$ and the length increased by ΔL, that is new length is ($L_{0} +$ΔL) and the new area is $A_{f}$ =(ΔL+$L_{0}$)(ΔL+$L_{0}$)

        that is $A_{f}=A_{0} ^{2}(1+2\alpha (T_{f} -T_{i} ))$

From the question, we have

the initial temperature $T_{i} =30$⁰C

the initial area $A_{0} =40cm^{2}$

coefficient of linear expansion $\alpha =24*10^{-6}$

final area $A_{f}=40cm^{2}$

so the final temperature

$T_{f} =T_{i}+\frac{A_{f}-A_{0} ^{2} }{A_{0} ^{2}*2*\alpha }$

$T_{f}=30-20*10^{3} =19.97*10^{3}$⁰C