Tag: black body radiation

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Multiple choice physics energy production perfectly black body black-body radiation 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 $T$ 

  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$
Reveal answer Fill a bubble to check yourself
D Correct answer
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,
$P = 1.0 e \sigma A T^4$.
Multiple choice physics energy production perfectly black body black-body radiation black body radiation

Emissivity of a perfect black body is

  1. always $0$.
  2. always $1$.
  3. between $0$ and $1$.
  4. always $>1$.
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $\epsilon=1$
Multiple choice physics energy production perfectly black body black-body radiation black body radiation

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

  1. black radiation.

  2. cavity radiation.

  3. Ferry's radiation.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  1. The cooling of earth at night

  2. Solar radiations

  3. Heat currents from a black surface

  4. None of these
Reveal answer Fill a bubble to check yourself
A,B Correct answer
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.
Multiple choice physics energy production perfectly black body black-body radiation 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)

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

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
According to wein's displacement law there is inverse relation between $\lambda _{max}$ of radiation emitted by black body and its temperature (absolute)
$\lambda _{max}\; \alpha \; \cfrac{1}{T} \Rightarrow =b\cfrac{1}{T} \Rightarrow \lambda _{max} T=b$
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The value of solar constant is approximately  :

  1. $ 1340\ watt/m^{2}$
  2. $ 430\ watt/m^{2}$
  3. $ 340\ watt/m^{2}$
  4. $ 1388\ watt/m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $2$($\dfrac{cal}{{cm}{\times} {min}}$)

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

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

  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 $2$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
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$

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

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

  1. $ A \propto 1/{d}^2$
  2. $\displaystyle A \propto \frac{1}{ d} $
  3. $ A \propto d$
  4. $ A \propto d^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
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. 

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

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

  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. $(97)^{\frac{1}{4}}T$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In steady state, the heat flux through each gap between the plates must be equal. Using the Stefan-Boltzmann law for radiative heat transfer between parallel plates, the heat flux q = sigma * (T1^4 - T2^4). Setting the flux between plate 1 and 2 equal to the flux between plate 2 and 3, we get (2T)^4 - T2^4 = T2^4 - (3T)^4. Solving for T2 gives T2 = ((2^4 + 3^4)/2)^(1/4) * T = (97/2)^(1/4) * T.