- #1

donbock

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## Homework Statement

(This is not a homework problem; it comes from a real-world problem I'm trying to solve.)

Sunlight is falling on an absorptive object. What will be equilibrium temperature of the object given the solar irradiance (I) and the ambient temperature?

I = solar irradiance = 1120 W/m[itex]^{2}[/itex] (from MIL-STD-810G).

## Homework Equations

My guess is that thermal equilibrium is reached when the energy flowing into the object from solar irradiance is balanced by the gray-body energy radiated from the object.

Radiated energy is given by the Stefan-Boltzmann Law:

P/A = e * [itex]\sigma[/itex] * (T[itex]^{4}[/itex] - T[itex]_{a}[/itex][itex]^{4}[/itex])

P/A = energy radiated per second per unit area (W/m[itex]^{2}[/itex]). Set this equal to I.

e = emissivity of the object = 0.93.

[itex]\sigma[/itex] = the Stefan-Boltzmann Constant (5.67 x 10[itex]^{-8}[/itex] W/m[itex]^{2}[/itex]/K[itex]^{4}[/itex])

T = temperature of the object (degrees Kelvin)

T[itex]_{a}[/itex] = ambient temperature (degrees Kelvin)

To use this formula I will also have to be given the emissivity (e) of the object.

## The Attempt at a Solution

This assumes the object absorbs all infalling solar irradiance (no reflection, no transmission).

This ignores convective cooling.

This ignores conductive cooling.

Solving for T as a function of T[itex]_{a}[/itex] yields the following results. (Notice I converted the temperatures to Celsius in the following list.)

T[itex]_{a}[/itex] (degC), T (degC):

0, 132

20, 138

40, 146

60, 155

80, 165

100, 176

These results don't feel plausible: I've never seen an object heated above the boiling point simply by letting the sun shine on it.

Is my approach all wrong?

Are the counterintuitive results solely due to the effects of my three assumptions?

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