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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