Tag: black body radiation

Questions Related to black body radiation

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$

Show answer
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 $>1$.

Show answer
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, $\epsilon=1$

Radiation coming from the hole of a Ferry's Black body is called 

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

  1. black radiation.

  2. cavity radiation.

  3. Ferry's radiation.

  4. None of these

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Correct Option: B
Explanation:
$\rightarrow$ Radiation coming from the hole of ferry's black body is called cavity radiation because this black body is double walled evacuated spherical cavity whose inner wall is blackened

Which of the following is an example of a black body radiation?

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

  1. The cooling of earth at night

  2. Solar radiations

  3. Heat currents from a black surface

  4. None of these

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Correct Option: A,B
Explanation:
The Earth is heated by the flux of energy it receives from sun and cools down by emitting infrared radiations to space. So we can say that cooling of earth is example of the black body radiation.
Sun has no solid surface, any radiation that hits the Sun is scattered and absorbed until it is completely lost. This makes the Sun very close to black bodies as far as absorption is concerned and as a result it would be reasonable to suppose that it is black body radiators.
So, the radiation of sun is the black body radiation.

The Wien's displacement law for a black body is
($T$ is the absolute temperature in $K$
$b$ is a constant of proportionality 
$e$ is the emissivity of the black body)

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

  1. $\lambda _{max} T = b$

  2. $\lambda _{max} T = e$

  3. $\lambda _{max} b = T$

  4. None of these

Show answer
Correct Option: A
Explanation:
According to wein's displacement law there is inverse relation between $\lambda _{max}$ of radiation emitted by black body and its temperature (absolute)
$\lambda _{max}\; \alpha \; \cfrac{1}{T} \Rightarrow =b\cfrac{1}{T} \Rightarrow \lambda _{max} T=b$

The value of solar constant is approximately  :

stefan's law black body radiation heat transfer thermal properties physics

  1. $ 1340\ watt/m^{2}$

  2. $ 430\ watt/m^{2}$

  3. $ 340\ watt/m^{2}$

  4. $ 1388\ watt/m^{2}$

Show answer
Correct Option: D
Explanation:

The solar constant is defined as the amount of heat energy received per second per unit area by a perfect black body placed at the surface of the Earth with its surface being held perpendicular to the direction of the sun's rays.

The value of solar constant is $1388$($\dfrac{watt}{{meter}^{2}}$) or $2$($\dfrac{cal}{{cm}{\times} {min}}$)

A heated body emits radiation which has maximum intensity at frequency $v _m$. If the temperature of the body is doubled

stefan's law black body radiation heat transfer thermal properties physics

  1. the maximum intensity radiation will be at frequency $2v _m$

  2. the maximum intensity radiation will be at frequency $\displaystyle\dfrac{1}{2}v _m$

  3. the total emitted energy will increase by a factor of $16$

  4. the total emitted energy will increase by a factor of $2$

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Correct Option: A,C
Explanation:

Wien's displacement law states maximum intensity wavength $ \lambda _{m}\propto \dfrac{1}{T}$
Also for any photon,$ \lambda \propto \dfrac{1}{\nu}$
Hence, frequency $\nu _m \propto T$
Doubling of temperature leads to doubling of frequency from $\nu _m$ to $ 2\nu _m$
From Stefan's law, power is directly proportional to $T^4$
Hence $ T \rightarrow 2T \Rightarrow E \rightarrow (\dfrac {2T}{T})^4E=16E$

The amount of radiations emitted by a black body depends on its

stefan's law black body radiation heat transfer thermal properties physics

  1. size

  2. mass

  3. temperature

  4. density

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Correct Option: C
Explanation:

The radiations emitted by the body only depend on the type of surface emitting and the temperature difference between the body and the surroundings.

The amplitudes of radiations from a cylindrical heat source is related to the distance are

stefan's law black body radiation heat transfer thermal properties physics

  1. $ A \propto 1/{d}^2$

  2. $\displaystyle A \propto \frac{1}{ d} $

  3. $ A \propto d$

  4. $ A \propto d^2$

Show answer
Correct Option: B
Explanation:

The intensity is inversely proportional to  square of distance and intensity is directly proportional to square of amplitude. So, amplitude is inversely proportional to distance. 

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

stefan's law black body radiation heat transfer thermal properties physics

  1. $(\cfrac{65}{2})^{\frac{1}{4}}T$

  2. $(\cfrac{97}{4})^{\frac{1}{4}}T$

  3. $(\cfrac{97}{2})^{\frac{1}{4}}T$

  4. $(97)^{\frac{1}{4}}T$

Show answer
Correct Option: C