Question

Find the increase in temperature of aluminium rod if its length is to be increased by 1%. (a for aluminium = 25 × 10⁻⁶/ ° C)

Answer 1

We will take the Length of the aluminium bar = L

Change in length (ΔL) = L/100

linear thermal expansion formula: ΔL/L = αΔT

                      α = Coefficient of linear expansion = 25 x 10⁻⁶/⁰C

                      ΔT= Temperature difference

                     

         (L/100)/L =  (25 × 10⁻⁶)(ΔT)

         ΔT  = (1/100)/(25 × 10⁻⁶)

         ΔT  = 400 ⁰C

Answer 2

"Solution:

Given:

Consider the Length of the aluminium rod = L

Thus, Change in length $(\Delta L) =\frac{ L}{100}$

The change in length is propotional to the orginal length and inversely propotional to the cross section "area of the rod".

We know that,

Linear thermal expansion formula:

The difference in length is directly propotional to the temprature change.

            $\frac{(\Delta L)}{L} = \alpha \Delta T$

         $\frac{\frac{L}{100}}{L} = (25 \times 10^{-6}) (\Delta T)$

             $\Delta T = \frac{1}{100} \times 25 \times 10^{-6}$

             $\Delta T = 400 \quad degree\quad Celsius$"