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Question

Two spheres of the same material have radii $$1m$$ and $$4m$$ and temperature $$4000K$$ and $$2000K$$ respectively. The energy radiated per second by the first sphere is :


A
greater than that of the second
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B
less than that of the second
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C
equal in both cases
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D
the information is incomplete to draw any conclusion
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Solution

The correct option is C equal in both cases
By Stefan's Law: 
Power $$={\sigma A e {T}^{4}}$$
$$e$$ is same for both the bodies. $$\sigma$$ is known as Stefan's constant
$$\dfrac{P_1}{P_2} =\dfrac{A_1 T_1^4}{A_2 T_2^4}$$
$$\dfrac{ A_1}{A_2} = \dfrac{r_1^2}{r_2^2} = \dfrac{1}{16}$$
$$\dfrac{T_1^4}{T_2^4}=\dfrac{16}{1}$$

By the above equations we get: $$P_1=P_2$$

Physics

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