Question

At 127${}^o$C radiated energy is $2.7\times {10}^{-3}J/s$. At what tempterature radiated energy is $4.32\times {10}^{6}J/s$?

• A. 400 K
• B. 4000 K
• C. 80000 K
• D. 40000K

Answer 1

The correct option is C 80000 K

Temperature $T_1={127}^{o}C=127+273=400K$

Energy radiated from a body
$Q=Ae\sigma T^{4}t$
$\Rightarrow \frac{Q_2}{Q_1}={\left(\frac{T_2}{T_1}\right)}^4$
$\Rightarrow \frac{T_2}{T_1}={\left(\frac{Q_2}{Q_1}\right)}^{1/4}={\left(\frac{4.32\times {10}^6}{2.7\times {10}^{-3}}\right)}^{1/4}$
$\frac{T_2}{400}={(\frac{16\times 27}{27}\times {10}^8)}^{1/4}=2\times {10}^2$
$\Rightarrow T_2=200\times 400=80000K$