Question

Rate of emission of a black body at ${546}^{\circ }C$ is $E$. Then the rate of emission of radiation of body at $0^{\circ }C$ will be

• A. $81E$
• B. $3E$
• C. $\frac{E}{3}$
• D. $\frac{E}{81}$

Answer 1

The correct option is D $\frac{E}{81}$

By Stefan Boltzmann law
we have
$E\propto T^4$

Rate of emission of a black body at ${546}^{\circ }C$ is
$E\propto (546+273{)}^4\propto (819{)}^4$
Rate of emission of a black body at $0^{\circ }C$ is
$E_o\propto (0+273{)}^4\propto (273{)}^4$

$\Rightarrow \frac{E_o}{E}={\left(\frac{273}{819}\right)}^4$

$\Rightarrow E_o=\frac{E}{81}$