Tag: stefan's law

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Questions Related to stefan's law

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.

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

The energy emitted by a black body at $727^oC$ is E. If the temperature of the body is increased by $227^oC$, the emitted energy will become

  1. 13 times

  2. 2.27 times

  3. 1.9 times

  4. 3.9 times
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here we know that energy emitted by any body is given by ${E}=\sigma{T^{4}}$

So, at temperature ${T}={727}^{o}C$ energy emitted will be ${E}$
at temperature ${T} _{1}={727+227}={954}^{o}C$ energy emitted will be ${E} _{1}={\sigma}{T} _{1}^{4}$
$\dfrac { E }{ { E } _{ 1 } } =\dfrac { { T }^{ 4 } }{ { T } _{ 1 }^{ 4 } }$
${ E } _{ 1 }=\dfrac { E\times { T } _{ 1 }^{ 4 } }{ { T }^{ 4 } } =\dfrac { E\times { 954 }^{ 4 } }{ { 727 }^{ 4 } } =2.96E$

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

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperature of the sun and star $A$ are $6000:K$ and $2000:K$, respectively, the ratio of the radii of the star $A$ and the sun is

  1. $300:1$

  2. $600:1$

  3. $900:1$

  4. $1200:1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Stars can be approximated as black bodies.
Hence by stefan's law, power emitted=P=$\sigma AT^4$
Thus,$ \dfrac{P _A}{P _{sun}}=\dfrac{r _A^2T _A^4}{r _{sun}^2T _{sun}^4}$
$\Rightarrow (\dfrac{r _A}{r _{sun}})^2=10000\times (\dfrac{6000}{2000})^4 \rightarrow \dfrac{r _A}{r _{sun}}=900$
So required ratio is 900:1
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

In pyrometer , temperature measured is proportional to $\underline{\hspace{0.5in}}$ energy emitted by the body 

  1. light

  2. electric

  3. radiation

  4. All the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Stefan- Boltzann law, $j^{ \star  }=\varepsilon \sigma T^{ 4 }$ connects temperature T with thermal radiation or irradiance  $j^{ \star  }$.
Thus measuring the irradiance with pyrometer yields the temperature of the body.

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

Two bodies of same shape and having emissivities 0.1 and 0.9 respectively radiate same energy per second. The ratio of their temperature is :

  1. $\sqrt{3}:1$

  2. $1:\sqrt{3}$

  3. $3:1$

  4. $1:3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\dfrac{E}{t}=e \sigma A T^4$
From above equation which is Stefan's Law of radiation, it is clear that:
$\dfrac{E _1}{E _2} = \dfrac{{e} _{1}\sigma{T} _{1}^{4}}{{e} _{2}\sigma{T} _{2}^{4}}$

$1 = \dfrac{{0.1}{T} _{1}^{4}}{{0.9}{T} _{2}^{4}}$

$\dfrac{{T} _{1}}{{T} _{2}} = \dfrac{\sqrt{3}}{1} $
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Two bodies A and B are kept in an evacuated chamber at $27^oC$. The temperature of A and B are $327^oC$ and $427^oC$ respectively. The ratio of rate of loss of heat from A and B will be

  1. 0.25

  2. 0.52

  3. 1.52

  4. 2.52
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The power radiated is directly proportional to fourth power of absolute temperature.
i.e.
$P \propto T^{4}$
$\frac{P _{1}}{P _{2}} = (\frac{T _{1}}{T _{2}})^{4}$
$\frac{P _{1}}{P _{2}} = (\frac{327+273}{427+273})^{4} = 0.53$
Hence the ratio of rate of heat loss = 0.53
Hence option B is correct.