Question

An ideal radiator at $0^{\circ }C$ radiates energy at the rate of $3.2\times {10}^{4}erg/c{m}^2-s$. Amount of heat radiated per second by a sphere of radius $4cm$ and at a temperature of ${1000}^{\circ }C$ is :

• A. $3.042\times {10}^{9}erg/s$
• B. $2.024\times {10}^{8}erg/s$
• C. $3.042\times {10}^{8}erg/s$
• D. $2.024\times {10}^{9}erg/s$

Answer 1

The correct option is A $3.042\times {10}^{9}erg/s$

Given,

$P_{\text{at 273 K}}=3.2\times {10}^{4}erg/c{m}^2-s.$

We know,

$P=\sigma T^4$ (taking ideal radiation case(e=1) )

$\sigma =\frac{3.2\times {10}^4}{(273{)}^4}$

Now at $1273K$,

$P=\frac{E}{A}=\sigma (1273{)}^4$

$E=\frac{3.2\times {10}^4\times (1273{)}^4\times 4\pi 4^2}{(273{)}^4}$

$E=6.43\times {10}^6\times 472.78=3042.33\times {10}^6$

$E=3.042\times {10}^{9}erg/s$

Hence option $\text{A}$ is the correct answer.