# Suppose that a steel hoop could be constructed to fit just around the earth's equator at a...

## Question:

Suppose that a steel hoop could be constructed to fit just around the earth's equator at a temperature of 20.0Celsius. What would be the thickness of space between the hoop and the earth if the temperature of the hoop were increased by 0.200C? Use {eq}6.38*10^6 {/eq}m for the radius of the Earth, and {eq}1.20*10^{-5}K^-1 {/eq} for the coefficient of linear expansion of steel.

## Thermal Expansion:

When the temperature of a metallic rod is increased the inter molecular distance increases and the length of conductor is slightly increased. The change in length depends on the original length and rise in temperature. The proportionality constant is called the coefficient of thermal expansion.

Given:

coefficient of thermal expansion, {eq}\alpha =1.2 \times 10^{-5}\ /K {/eq}

Radius of earth, {eq}R=6.38 \times 10^6\ m \\ \Delta T=0.4^\circ C {/eq}

The extended length of circumference of loop

{eq}=2 \pi R (1+ \alpha \times \Delta T ) \\ {/eq}

The thickness of space will be the change in radius of this loop, that is

{eq}= R \alpha \Delta T \\ =6.38 \times10^6 \times 1.2 \times 10^{-5} \times 0.4 \\ =30.624\ m {/eq} 