The temperature of a radiating body increases by 50 %. Then, the increase in the amount of radiation emitted will be approximately:

Question

The temperature of a radiating body increases by 50 %. Then, the increase in the amount of radiation emitted will be approximately: (A) 185 % (B) 385 % (C) 406 % (D) 607 %

Tardigrade Admin · Accepted Answer

Given that, Ti and Tf=1.5Ti So, E propto T4 Ei=kTi4 Ef=kTi4× 1.54=5.06Ti4 So, Δ E %=(Ti4 (. 5 . 06 .) - Ti4/Ti4)× 100=406 %

Q. The temperature of a radiating body increases by $50%.$ Then, the increase in the amount of radiation emitted will be approximately:

$185%$

$385%$

$406%$

$607%$

Given that, $T_{i}$ and $T_{f} = 1.5 T_{i}$
So, $E \propto T^{4}$
$E_{i} = k T_{i}^{4}$
$E_{f} = k T_{i}^{4} \times 1. 5^{4} = 5.06 T_{i}^{4}$
So, $Δ E % = \frac{T _{i}^{4} ( 5.06 ) - T _{i}^{4}}{T _{i}^{4}} \times 100 = 406%$

Q. The temperature of a radiating body increases by 50%. Then, the increase in the amount of radiation emitted will be approximately:

185%

385%

406%

607%