Question

Consider a 40,000 km steel pipe in the shape of a ring that fits snuggly all around the circumference of the Earth. We are heating now the ring so its temperature increased by 1 degree C. Now, the pipe will no longer be snug. How high the ring will now stand above ground level? (Make as many simplifications as necessary). Data: Coefficient of linear expansion for steel is 11^*10^-6 /degree C. This means, for example, that a 1-meter bar of steel that increases its temperature by 1 degree C will expand 11^*10^-6 meters (11 micrometers)

An electric fan not only does not decrease the temperature of the air, but it actually increases air temperature. How can you then explain that you are cooled by a fan on a hot day?

Answer 1

Solution:

1.) Using thermal expansion of solids,

L = L_iT , For steel = 11*10⁶/^oC

Given L = 40,000* 11*10^-6/^oC*1^oC = 0.44km = 440m

So, The final Lenght is,

L_f = 40,000km + 0.44km = 40,000.44km

We know tha circumfarence of circle is 2r

So, r_i = 400000/2 = 63661.97724km

r_f = 400000.44/2 = 63662.04726km

r = r_f - r_i = 0.0700km = 70m.

2.)Reason: You are cooled by the fan, which blows air over you to increase the rate of evaporation from your skin, but you are a small part of the overall system, which warms.

I hope you understood the problem, If yes rate me!! or else comment for a better solution.