Question

A metal rod has a length of 123. cm at 200°C. At what temperature will the length be 92.6 cm if the coefficient of linear expansion of the material in the rod is 2.0 x 10-5 °C-1?

Answer 1

`\theta_(2) = 15400^0 C`

Step-by-step explanation:

The formula for linear expansivity,
`\alpha = (l_(2) - l_(1) )/(l_(1) ( \theta_(2) - \theta_(1) ))`

original length, l₁ = 123 cm = 1.23 m

final length, l₁ = 92.6 cm =0.926 m

original temperature, θ₁ = 200°C

Linear expansivity, α = 2 * 10⁻⁵ °C⁻¹

Putting these values into the formula:

`2 * 10^(-5) = (1.23 - 0.926 )/(l_(1) ( \theta_(2) -200 ))\\ \theta_(2) -200 = (0.304)/(2 * 10^(-5) ) \\\theta_(2) = 15200 + 200\\\theta_(2) = 15400^0 C`