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16. ⇒ (MHT CET 2021 20th September Morning Shift )

A perfectly black body emits a radiation at temperature 'T $_{1}$ ' K. If it is to radiate at 16 times this power, its temperature 'T $_{2}$ ' K should be

A. 8T $_{1}$

B. 4T $_{1}$

C. 2T $_{1}$

D. 16T $_{1}$

Correct Option is (C)

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

$∴$ $16 = {(\frac{T_{2}}{T_{1}})}^{4}$

$∴$ $\frac{T_{2}}{T_{1}} = 2$

⇒Kinetic Theory of Gases