Heat and Thermodynamics 3 Question 34
34. The earth receives at its surface radiation from the sun at the rate of $1400 Wm^{-2}$. The distance of the centre of the sun from the surface of the earth is $1.5 \times 10^{11} m$ and the radius of the sun is $7 \times 10^{8} m$. Treating the sun as a black body, it follows from the above data that its surface temperature is …… K.
$(1989,2 M)$
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Answer:
Correct Answer: 34. 5803
Solution:
- Given, $\frac{\left(\sigma T^{4}\right)\left(4 \pi R^{2}\right)}{\left(4 \pi r^{2}\right)}=1400$
$$ \begin{aligned} \therefore T & =\left(\frac{1400 \times r^{2}}{\sigma R^{2}}\right)^{1 / 4} \\ & =\left[\frac{1400 \times\left(1.5 \times 10^{11}\right)^{2}}{\left(5.67 \times 10^{-8}\right) \times\left(7 \times 10^{8}\right)^{2}}\right]^{1 / 4} \\ & =5803 K \end{aligned} $$
