SATHEE: Heat and Thermodynamics 3 Question 34

Heat and Thermodynamics 3 Question 34

34. The earth receives at its surface radiation from the sun at the rate of $1400 W m^{- 2}$ . 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, $\frac{(σ T^{4}) (4 π R^{2})}{(4 π r^{2})} = 1400$

$\begin{aligned} ∴ T & = {(\frac{1400 \times r^{2}}{σ R^{2}})}^{1 / 4} \\ = {[\frac{1400 \times {(1.5 \times 10^{11})}^{2}}{(5.67 \times 10^{- 8}) \times {(7 \times 10^{8})}^{2}}]}^{1 / 4} \\ = 5803 K \end{aligned}$

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Heat and Thermodynamics 3 Question 34

Answer:

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