Rankers Physics

Uncategorized: Practice Problem & Solution

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 $Q$? (2012 Pre)
$Q/4\pi R^2\sigma$
$(Q/4\pi R^2\sigma)^{-1/2}$
$(4\pi R^2 Q/\sigma)^{1/4}$
$(Q/4\pi R^2\sigma)^{1/4}$

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Rate of energy production $Q = P = \sigma A T^4 = \sigma (4\pi R^2)T^4$. Therefore, $T = (\frac{Q}{4\pi R^2\sigma})^{1/4}$.

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