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

Answer:

$\theta_{2} = 15400^0 C$

Explanation:

The formula for linear expansivity, $\alpha = \frac{l_{2} - l_{1} }{l_{1} ( \theta_{2} - \theta_{1} )}$

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:

$2 * 10^{-5} = \frac{1.23 - 0.926 }{l_{1} ( \theta_{2} -200 )}\\ \theta_{2} -200 = \frac{0.304}{2 * 10^{-5} } \\\theta_{2} = 15200 + 200\\\theta_{2} = 15400^0 C$