Question

If the temperature of the body is increased by $ 10\%, $ the percentage increase in the emitted indication will be

• A. $ 46\% $
• B. $ 40\% $
• C. $ 30\% $
• D. $ 80\% $

Answer 1

Answer: (A)

$Q \propto T^{4} \Rightarrow \frac{Q_{1}}{Q_{2}}=\left(\frac{T_{1}}{T_{2}}\right)^{4}$
If $T_{1}=T$ then $T_{2}=T+\frac{10}{100} T=1.1 \,T$
$\frac{Q_{1}}{Q_{2}}=\left(\frac{T}{1.1 T}\right)^{4} $
$\Rightarrow Q_{2}=1.46 Q_{1}$
$\%$ increase in energy
$=\left(\frac{Q_{2}-Q_{1}}{Q_{1}}\right)$