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Q. No.The radius of a spherical black body is \(R,\) and \(\alpha\) represents the rate of energy production within the body. The temperature of the given black body in a steady-state is: (where \(\sigma\) is Stefan- Boltzmann constant)
| 1. | \(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)^{\dfrac{1}{4}} \) | 2. | \(\left(\dfrac{\sigma \times 4 \pi R^2}{\alpha}\right)^{\dfrac{1}{4}}\) |
| 3. | \(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)\) | 4. | \(\left(\dfrac{4 \pi R^2 \times \sigma}{\alpha}\right)\) |
Subtopic: Stefan-Boltzmann Law |
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Level 1: 80%+
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Two spheres \(A\) and \(B\) of same material having radius \(8\) cm and \(4\) cm are maintained at temperatures \(127^{\circ}\text{C}\) and \(527^{\circ}\text{C}\) respectively. The ratio of energy radiated by \(A\) and \(B\) is:
1. \(1:4\)
2. \(3:1\)
3. \(1:2\)
4. \(6:1\)
1. \(1:4\)
2. \(3:1\)
3. \(1:2\)
4. \(6:1\)
Subtopic: Stefan-Boltzmann Law |
84%
Level 1: 80%+
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A radiation blackbody has the shape of a sphere of radius \(r.\) Its surface is at a temperature \(T\) (in Kelvin). If the temperature is doubled and the radius is halved, the total rate of radiation emitted from the body:
| 1. | increases by a factor of \(4\) |
| 2. | increases by a factor of \(2\) |
| 3. | remains unchanged |
| 4. | decreases by a factor of \(2\) |
Subtopic: Stefan-Boltzmann Law |
82%
Level 1: 80%+
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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 |
65%
Level 2: 60%+
AIPMT - 2010
Hints
‘Gulab Jamuns’ (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice big (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following:
| 1. | Both size gulab jamuns will get heated in the same time. |
| 2. | Smaller gulab jamuns are heated before bigger ones. |
| 3. | Smaller pizzas are heated before bigger ones. |
| 4. | Bigger pizzas are heated before smaller ones. |
Subtopic: Stefan-Boltzmann Law |
Level 3: 35%-60%
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Q. No.
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