The Stefan-Boltzmann Law lets you relate how much energy something is radiating to its temperature (we did this multiple times in class). In this case we know how much energy the Earth was radiating and want to know what temperature is was,so we can use the formula \( T \) = fourth root of (Energy_out / (sigma)) where sigma = 5.67 " \( 10^{-8} \). If your calculator doesn't do a fourth root, Google will calculate this for you (as I demonstrated in lecture) by typing "fourth root of (XXX / (YYY))". What is the temperature, in Kelvin, of the Earth if it is radiating the Energy_out you just calculated in the previous question? Round your answer to the nearest Kelvin and please do not include units. You should get a 3-digit value for an answer. Your Answer:

To calculate the temperature of the Earth using the Stefan-Boltzmann Law, you would plug your \( Energy_{out} \) value into the formula \( T = \sqrt[4]{\frac{Energy_{out}}{5.67 \times 10^{-8}}} \). Assuming you’ve accurately calculated \( Energy_{out} \), just use the fourth root function as suggested. For example, if your \( Energy_{out} \) value is 1.0 x 10^3 watts, you would take the fourth root of \( \frac{1000}{5.67 \times 10^{-8}} \), which should yield a temperature in Kelvin when rounded to the nearest whole number. If you accidentally miscalculate or forget to convert units, you might end up with a value that's off by quite a bit! Double-check your \( Energy_{out} \) and ensure it’s in the correct units before making that final calculation. Google can help, but it's always good practice to verify each step to avoid common pitfalls.