Question 847: Thermodynamics & KTG

Question

A black sphere has radius '$$R$$' whose rate of radiation is '$$E$$' at temperature '$$T$$'. If radius is made $$R / 3$$ and temperature '$$3 T$$', the rate of radiation will be

Accepted Answer

$$E=e A \sigma T^4$$
But for sphere, $$A=4 \pi R^2$$
$$\begin{aligned}
	herefore \quad & E=e\left(4 \pi R^2ight) \sigma T^4 \
	herefore \quad & \frac{E_1}{E_2}=\frac{R_1^2 T_1^4}{R_2^2 T_2^4} \
	herefore \quad & \frac{E}{E_2}=\frac{R^2 T^4}{\left(\frac{R}{3}ight)^2(3 T)^4} \
	herefore \quad & E_2=9 E
\end{aligned}$$

Answer

E

Answer

3E

Answer

6E

Answer

9E

Thermodynamics & KTG

A black sphere has radius '$R' whose rate of radiation is 'E' at temperature 'T'. If radius is made R / 3 and temperature '3 T$', the rate of radiation will be

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