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 |
83%
From NCERT
AIPMT - 2012
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The total radiant energy per unit area, normal to the direction of incidence, received at a distance $$R$$ from the centre of a star of radius $$r,$$ whose outer surface radiates as a black body at a temperature $$T$$ K is given by: (Where $$\sigma$$ is Stefan’s constant):
1. $$\dfrac{\sigma r^{2}T^{4}}{R^{2}}$$

2. $$\dfrac{\sigma r^{2}T^{4}}{4 \pi R^{2}}$$

3. $$\dfrac{\sigma r^{2}T^{4}}{R^{4}}$$

4. $$\dfrac{4\pi\sigma r^{2}T^{4}}{R^{2}}$$

Subtopic:  Stefan-Boltzmann Law |
62%
From NCERT
AIPMT - 2010
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A black body at $$227^{\circ}~\mathrm{C}$$ radiates heat at the rate of $$7~ \mathrm{cal-cm^{-2}s^{-1}}$$.  At a temperature of $$727^{\circ}~\mathrm{C}$$, the rate of heat radiated in the same units will be:
1. $$60$$
2. $$50$$
3. $$112$$
4. $$80$$

Subtopic:  Stefan-Boltzmann Law |
86%
From NCERT
AIPMT - 2009
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Assuming the sun to have a spherical outer surface of radius $$r,$$ radiating like a black body at temperature $$t^\circ\text C,$$ the power received by a unit surface of the earth (normal to the incident rays) at a distance $$R$$ from the centre of the sun is: (where $$\sigma$$ is Stefan's constant.)
1. $$\dfrac{4\pi r^2\sigma t^4}{R^2}$$

2. $$\dfrac{r^2\sigma(t+273)^4}{4\pi R^2}$$

3. $$\dfrac{16\pi^2r^2\sigma t^4}{R^2}$$

4. $$\dfrac{r^2\sigma(t+273)^4}{R^2}$$

Subtopic:  Stefan-Boltzmann Law |
65%
From NCERT
AIPMT - 2007
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A black body is at $$727^\circ\text C.$$ It emits energy at a rate that is proportional to:
1. $$(727)^2$$
2. $$(1000)^4$$
3. $$(1000)^2$$
4. $$(727)^4$$

Subtopic:  Stefan-Boltzmann Law |
80%
From NCERT
AIPMT - 2007
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