Question

A spherical blackbody radiator with a diameter of 1.50 m is held at a constant temperature. What is the temperature (K) if the power radiated by the body is 18.0 kcal / min?

Answer 1

$\begin{gathered} P=e\sigma A(T^4-T^4_c) \\ \end{gathered}$

The first part is to transform the power from kcal/min to J/s

$\frac{18\text{kcal}}{\min}\cdot\frac{1\min}{60s}\cdot\frac{4186.8J}{1\text{kcal}}=\frac{1256.04J}{s}=1256.04W$

Now we can continue

e=1 due to is a blackbody

$\begin{gathered} 1256.04W=5.6703\cdot10^{-8}\cdot(\pi\cdot\frac{1.5^4}{4})\cdot(T)^4 \\ 5571120034=T^4 \\ T=273.203K \end{gathered}$