NEET Questions Solved

NEET - 2012

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

(a)$Q/4{\mathrm{\pi R}}^{2}\mathrm{\sigma }$

(b)${\left(Q/4{\mathrm{\pi R}}^{2}\mathrm{\sigma }\right)}^{-1/2}$

(c)${\left(4{\mathrm{\pi R}}^{2}\mathrm{Q}/\mathrm{\sigma }\right)}^{1/4}$

(d)${\left(Q/4{\mathrm{\pi R}}^{2}\mathrm{\sigma }\right)}^{1/4}$

From Stefan' law,

$E=\sigma {T}^{4}$

So, the rate energy production

$Q=E×A$

$Q=\sigma {T}^{4}×4{\mathrm{\pi R}}^{2}$

Temperature of star

$T={\left(\frac{Q}{4{\mathrm{\pi R}}^{2}\mathrm{\sigma }}\right)}^{1/4}$

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