Solution:

The energy emitted by a black body is proportional to the fourth power of its absolute temperature, as per Stefan-Boltzmann Law:

\[
P \propto T^4
\]

Step 1: Convert temperature to kelvins

The temperature of the black body is \(727^\circ C\), which is:

\[
T = 727 + 273 = 1000\,K
\]

Step 2: Apply Stefan-Boltzmann Law

Since the energy emitted is proportional to \(T^4\):

\[
P \propto (1000)^4
\]

Thus, the rate of energy emission is proportional to \((1000)^4\).