Question

What temperature change is required to change the length of a 5.5 m steel beam by 0.0012 m? Hint: α of steel = 12 x 10-6k-1

Answer 1

Given:

• Length of steel = 5.5 m
• Increase in length = 0.0012 m
• α of steel = 12 x 10-6/K

To find:

Temperature change needed ?

Calculation:

• Let the required temperature change be ∆T.

$\Delta L = L \times \alpha \times \Delta T$

$\implies \: \Delta T = \dfrac{\Delta L}{ L \alpha }$

$\implies \: \Delta T = \dfrac{0.0012}{ 5.5 \times (12 \times {10}^{ - 6} )}$

$\implies \: \Delta T = \dfrac{12 \times {10}^{ - 4} }{ 5.5 \times (12 \times {10}^{ - 6} )}$

$\implies \: \Delta T = 0.181 \times {10}^{2}$

$\implies \: \Delta T = 18.1 \: K$

So, temperature change of 18.1 Kelvin is required.