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Stefan Boltzmann Law MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Stefan Boltzmann law is considered one of the most asked concept.

  • 6 Questions around this concept.

Solve by difficulty

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U1,  at wavelength 500 nm is U2 and that at 1000 nm is U3. Wien's constant, b = 2.88 \times 106 nmK. Which of the following is correct?

A spherical black body with a radius of 12 cm radiates 450-watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be :

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q ?
( σ stands for Stefaris constant)

A black body at 227°C radiates heat at the rate of 7 Cals/cm2s. At a temperature of 727°C, the rate of heat radiated in the same units will be:

Concepts Covered - 0

Stefan Boltzmann law

 

  • According to Stefan Boltzmann law, the radiant energy emitted by a perfectly black body per unit area per sec is directly proportional to the fourth power of its absolute temperature,

       or emissive power of the black body is directly proportional to the fourth power of its absolute temperature (\theta).

     i.e  E\;\alpha\; \theta^{4}

          \Rightarrow\ E=\sigma\theta^{4}

where 

\sigma=Stefan's constant

and its value is

\sigma=5.67\times 10^{-8}W/m^{2}K^{4}

  • For ordinary body

            1.  Emissive power is  given by  e=\epsilon E

           So according to Stefan Boltzmann law

   e=\epsilon E=\epsilon \sigma \theta^{4}

where  \epsilon = represent emissivity of the material

2. Radiant energy-

If Q is the total energy radiated by the ordinary body then

e= \frac{Q}{A\times t}=\epsilon \sigma \theta^{4}\Rightarrow Q=A\epsilon \sigma \theta^{4}t

3. Radiant power (P): It is defined as the energy radiated per unit area.

i.e   P=\frac{Q}{t}=A\epsilon \sigma \theta^{4}

4.  If an ordinary body at temperature \theta is surrounded by a body at a temperature  \theta _0

                    Then according to Stefan Boltzmann law

                                e =\epsilon \sigma (\theta^{4}-\theta_0^{4})

 

 

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