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(1\min)/(60s)\cdot\frac{4186.8J}{1\text{kcal}}=(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(1.5^4)/(4))\cdot(T)^4 \\ 5571120034=T^4 \\ T=273.203K \end{gathered}`