Question

The rate of emission of a black body at $0^{0}C$ is R. Its rate of emission at ${273}^0$C is

• A. 4R
• B. 8R
• C. 16R
• D. 32R

Answer 1

The correct option is C 16R

For rate of emission of black body, $\varphi \propto T^4$

At $0^{o}C$ i.e. $273K;\varphi =R$

At ${273}^{o}C$ i.e. $546K;\varphi =?$

$\frac{{\varphi }_1}{{\varphi }_2}=\frac{{T_1}^4}{{T_2}^4}\Rightarrow \frac{R}{{\varphi }_2}=\frac{{\left(273\right)}^4}{{(2\times 273)}^4}=\frac{{\left(273\right)}^4}{{\left(273\right)}^4\times 2^4}\Rightarrow {\varphi }_2=2^{4}R=16R$

Required rate of emission at ${273}^{o}C$ is $16R$.