Tag: black-body radiation

Questions Related to black-body radiation

Temp. of black body is $3000K$ when black body cools. Then change in wavelength $\Delta \lambda=9$ micron corresponding to maximum energy density. Now temp. of black body is:

physics energy production perfectly black body black-body radiation black body radiation

  1. $300K$

  2. $2700K$

  3. $270K$

  4. $1800K$

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Correct Option: A

The rate of emission of radiation of a black body at 273$^{ \circ  }{ C }$ is E, then the rate of emission of radiation  of this body at 0$^{ \circ  }{ C }$ will be :-

physics energy production perfectly black body black-body radiation black body radiation

  1. $\dfrac { E }{ 16 } $

  2. $\dfrac { E }{ 4 } $

  3. $\dfrac { E }{ 8 } $

  4. 0

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Correct Option: A

For non black bodies, the range of values of emissivity $e$ is 

physics energy production perfectly black body black-body radiation black body radiation

  1. $- 1 < e < 1 $

  2. $- 1 < e < 0 $

  3. $ 1 < e < 2 $

  4. $0 < e < 1 $

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Correct Option: D

A blackbody does not

physics energy production perfectly black body black-body radiation black body radiation

  1. emit radiation

  2. absorb radiation

  3. reflect radiation

  4. refract radiation

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Correct Option: B

An ideal black body is a :

physics energy production perfectly black body black-body radiation black body radiation

  1. lump of charcoal heated to a high temperature

  2. metal coated with a black dye

  3. glass surface coated with coal tar

  4. hollow enclosure blackened inside and having a small hole

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Correct Option: D
Explanation:

Hollow enclosure blackened inside and having a small hole is a very good example of a black body.
Suppose once light enters inside it.
It may be absorbed or it may be reflected.
Since it is blackened from inside, there is a high probability that it will be absorbed.
Now if it is reflected, it will suffer multiple reflections and it is very unlikely that it will come out of the hole because the aperture of hole is too small. Moreover, with each reflection, more and more fraction of it will be absorbed. So, it will serve as a good black body.

Which of the following is more close to a black body?

physics energy production perfectly black body black-body radiation black body radiation

  1. Black board paint

  2. Green leaves

  3. Black holes

  4. Red roses

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Correct Option: C
Explanation:

we know that $\alpha +\rho +\tau =1$
${\alpha}= absorptivity$
${\rho}=reflectivity$
${\tau}=transmitivity$
so for black body ${\rho}\  and \ {\tau} \ will\  be \ zero$
so ${\alpha}=1$ so black hole has also ${\alpha}=1$ which is equivalent to black body.

Hence we can consider black holes as black body.

Initially a black body at absolute temperature $T$ is kept inside a closed chamber at absolute temperature $T _{o}$. Now the chamber is slightly opened to allow sun rays to enter. It is observed that temperatures $T$ and $T _{o}$ remains constant.Which of the following statement is/are true?

physics energy production perfectly black body black-body radiation black body radiation

  1. The rate of emission of energy from the black body remains the same

  2. The rate of emission of energy from the black body increases

  3. The rate of absorption of energy by the black body increases.

  4. The energy radiated by the black body equals the energy absorbed by it

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Correct Option: A,D
Explanation:

It is given that the absolute temperatures of both the black body and the surroundings are constant with time, even after sunlight(radiation) is incident on it.

  • When a body absorbs radiation, its temperature increases
  • When a body emits radiation, its temperature decreases
Also the sun, being a source of infinite radiation(very large source of radiation).
We infer from this that the incident radiation should be of constant magnitude.
And if the temperature of the black body is a constant, that means it's emission and absorption of radiation are matched and equal. The absorption is of constant magnitude, because the sun's radiation is of constant value. Hence the emission is of constant value also and is equal to the absorption. The options follow.

An ideal black body at room temperature is thrown in a furnace. It is observed that

physics energy production perfectly black body black-body radiation black body radiation

  1. initially it is darkest body and at later time the brightest

  2. it is darkest body at all the times

  3. it cannot be distinguished at all the times

  4. initially it is the darkest body and at later times it cannot be distinguished

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Correct Option: D
Explanation:

Initially the black body is in bright environment. So, it appears dark and finally when its temperature becomes equal to temperature of furnace, it becomes invisible

A spherical body of area A and emissivity $e = 0.6$ is kept inside a perfectly black body. Total heat radiated by the body at temperature $T$ 

physics energy production perfectly black body black-body radiation black body radiation

  1. $ 0.8\ e\sigma AT^4$

  2. $ 0.4\ e\sigma AT^4$

  3. $ 0.6\ e\sigma AT^4$

  4. $ 1.0\ e\sigma AT^4$

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Correct Option: D
Explanation:
According to Stefan's Boltzman law, the thermal energy radiated by a black body radiator per second per unit area is proportional to fourth power of the absolute temperature and is given by
$\dfrac{P}{A} = \sigma T^4$ ..............(1)
For the hot bodies other than black body radiator equation (1) becomes,
$\dfrac{P}{A} = e \sigma T^4$
$P = e \sigma A T^4$ .................(2)
where, $e$ is the emissivity of the body.
Now, when such hot body is kept inside a perfectly black body, the total thermal radiation is the sum of emitted radiations (in open) and the part of incident radiations reflected from the walls of the perfectly black body. This will give black body radiations, hence the total radiations emitted by the body will be,
$P = 1.0 e \sigma A T^4$.

Emissivity of a perfect black body is

physics energy production perfectly black body black-body radiation black body radiation

  1. always $0$.

  2. always $1$.

  3. between $0$ and $1$.

  4. always $>1$.

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Correct Option: B
Explanation:
Emissivity of a perfect black body is always 1.
The best absorber is defined as the object which can absorb all the electromagnetic radiations falling upon it. The black body is not only a perfect absorber but it is also the best in emitting radiation. Also, a black bosy in thermal equlibrium has emissivity, $\epsilon=1$