Question

Energy is being emitted from the surface of a black body at $127^{\circ} C$ the rate of $1.0 \times 10^{6} J / sm ^{2} .$ The temperature of black body at which the rate of energy emission is $16.0 \times 10^{6} J / sm ^{2}$ will be

• A. $754^{\circ} C$
• B. $ 527^{\circ} C$
• C. $ 254^{\circ} C$
• D. $ 508^{\circ} C$

Answer 1

Answer: (B)

$\frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right.)^{4} $
$ \frac{T_{2}}{T_{1}} =\left(\frac{E_{2}}{E_{1}}\right)^{1 / 4}$
$=\left[\frac{16.0 \times 10^{6}}{1.0 \times 10^{6}}\right]^{1 / 4}=2 $
$T_{2} =2 T_{1}=2 \times T_{1} $
$=2 \times 400$
$=800 \,K =527^{\circ} C $