Question
A black body is at $${727^ \circ }C.$$ It emits energy at a rate which is proportional to
A.
$${\left( {1000} \right)^4}$$
B.
$${\left( {1000} \right)^2}$$
C.
$${\left( {727} \right)^4}$$
D.
$${\left( {727} \right)^2}$$
Answer :
$${\left( {1000} \right)^4}$$
Solution :
According to Stefan's law,
$$\eqalign{
& E \propto {T^4} \cr
& \propto {\left( {t + 273} \right)^4}K\,\,\left[ {{{727}^ \circ }C = \left( {727 + 273} \right)K} \right] \cr
& \propto {\left( {727 + 273} \right)^4}K \cr
& \propto {\left( {1000} \right)^4}K \cr} $$