If the radius of a star is $$R$$ and it acts as a black body, what would be the temperature of the star at which the rate of energy production is $$Q$$?
1. $$\frac{Q}{4\pi R^2\sigma}$$
2. $$\left(\frac{Q}{4\pi R^2\sigma}\right )^{\frac{-1}{2}}$$
3. $$\left(\frac{4\pi R^2 Q}{\sigma}\right )^{\frac{1}{4}}$$
4. $$\left(\frac{Q}{4\pi R^2 \sigma}\right)^{\frac{1}{4}}$$

Subtopic:  Stefan-Boltzmann Law |
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AIPMT - 2012
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A spherical black body with a radius of 12 cm radiates 450-watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watts would be:

 1 225 2 450 3 1000 4 1800
Subtopic:  Stefan-Boltzmann Law |
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NEET - 2017
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If the sun’s surface radiates heat at $6.3×{10}^{7}$ then the temperature of the sun, assuming it to be a black body, will be:
$\left(\mathrm{\sigma }=5.7×{10}^{-8}\right)$ ${\mathrm{Wm}}^{-2}{\mathrm{K}}^{-4}$
1. $5.8×{10}^{3}$ $\mathrm{K}$
2. $8.5×{10}^{3}$ $\mathrm{K}$
3. $3.5×{10}^{8}$ $\mathrm{K}$
4. $5.3×{10}^{8}$ $\mathrm{K}$

Subtopic:  Stefan-Boltzmann Law |
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