Question

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 (c stands for stefan "s constant) ?????????????????

Answer 1

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 $q$ (c stands for Stefan "s constant)

Solution

Total surface area of the star

$$A = 4 \pi R ^ {2}.$$

By Stefan – Boltzmann black body kept at temperature $T$ radiates heat per unit surface area per second given by

$$E = c T ^ {4},$$

$c$ - Stefan-Boltzmann constant.

Now

$$E = \frac {q}{A} = \frac {q}{4 \pi R ^ {2}} \rightarrow \frac {q}{4 \pi R ^ {2}} = c T ^ {4}.$$

The temperature of the star

$$T = \sqrt [ 4 ]{\frac {q}{4 \pi c R ^ {2}}} = \frac {1}{\sqrt {2 R}} \sqrt [ 4 ]{\frac {q}{\pi c}}.$$

Answer: $\frac{1}{\sqrt{2R}} \sqrt [4]{\frac{q}{\pi c}}$.