Question

If the temperature of a body increases by $2$% then energy radiated will increase by

• A. 2%
• B. 8%
• C. 4%
• D. 16%

Answer 1

Answer: (B)

8%

We know that by $Stefa{n}^{\prime }s$ $law$,

Energy Radiated $\alpha$ $T^4$

$E=k{T}^4$

Given temperature is increased by 2%

Percentage change in Energy = $\frac{{T^4(1+0.02)}^4-T^4}{T^4}\times 100$

Using binomial theorem $(1+0.02{)}^4$ can be approximated to $1.08$

Using this in the above formula we get,

Percentage Change in Energy=$8\%$