If temperature of a black body increases from 300 K to 900 K , then the rate of energy radiation increases by

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Question: Answered & Verified by Expert

If temperature of a black body increases from

300 K

to

900 K

, then the rate of energy radiation increases by

PhysicsThermal Properties of MatterBITSATBITSAT 2017

Options:

A $81$
B $3$
C $9$
D $2$

Solution:

2178 Upvotes Verified Answer

The correct answer is:

81

According to Stefan's law $ρ = \frac{E}{t} = σ A e T^{4}$

So, we can write as

$\frac{E_{2}}{E_{1}} = {(\frac{T_{2}}{T_{1}})}^{4}$

$\frac{E_{2}}{E_{1}} = {(\frac{900}{300})}^{4} \Rightarrow \frac{E_{2}}{E_{1}} = {(3)}^{4}$

$E_{2} = 81 E_{1} \Rightarrow \frac{E_{2}}{E_{1}} = 81$

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