If you lie on the ground at night with no cover, you get cold rather quickly. Much of this is due to energy loss by radiation. At night in a dry climate, the temperature of the sky can drop to −40∘C. If you are lying on the ground with thin clothing that provides little insulation, the surface temperature of your skin and clothes will be about 30∘C. Estimate the net rate at which you body loses energy by radiation to the night sky under these conditions. Hint: What area should we use?

301.48 J/s

Explanation:

We are given;

Temperature of the sky dropping to −40∘C: T_o = -40°C = -40 + 273 = 233 K

Temperature of your skin and clothes: T = 30°C = 30 + 273 = 303 K

Body surface area of human body is around 2 m². But here only half of the body is facing the sky, Thus Area is: A = 2/2 = 1 m²

To solve this, we will use the equation for thermal heat transfer known as the Stefan bolt Mann equation.

ΔQ/Δt = εσA(T⁴ - (T_o)⁴)

Where;

ΔQ/Δt is the rate at which you body loses energy by radiation

ε is the emissivity of the human body with a value of 0.97

σ is Stefan boltzmann constant with a value of 5.67 X 10^(-8) W/m².K⁴

Thus;

ΔQ/Δt = 0.97 × 5.67 X 10^(-8) × 1(303⁴ - 233⁴)

ΔQ/Δt = 301.48 J/s

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it