Suppose that a steel hoop could be constructed to fit just around the earth’s equator at 20.0o C. What would be the thickness of space between the hoop and the earth if the temperature of the hoop were increased by 0.500 Co?

Solution 76P The radius of the earth is 6371000 meters. The diameter is, 12742000 meters. The coefficient of linear expansion for steel is, 6 1 = 11 × 10 K The temperature increased by, 0 T = 0.500 C The change in length will be, 11 LL = T = 11 × 10 × 0.500 change in diameter = 11 × 10 11 × 0.500 × diameter of earth = 11 × 10 11× 0.500 × 12742000 = 0.00070081 meters. CONCLUSION: So, the gap between earth and hoop is 0.00070081 meters.