Tag: stefan's law

Questions Related to stefan's law

The Sun delivers ${{10}^{3}}W/{{m}^{2}}$ of electromagnetic flux to the Earth's surface.The total power that is incident on a roof of dimensions $8m\times 20m$, will be

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

  1. $6.4\times { 10 }^{ 3 }W$

  2. $3.4\times { 10 }^{ 4 }W$

  3. $1.6\times { 10 }^{ 5 }W$

  4. none of these

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Correct Option: C
Explanation:

Here the power per unit area is given, $I=10^3  W/m^2$

So, the total power $=I\times $ area of roof $=10^3\times (8\times 20)=1.6\times 10^5 W$ 

Choose the correct relation, when the temperature of an isolated black body falls from $T _{1}$ to $T _{2}$ in time $'t'$, and assume $'c'$ to be a constant.

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

  1. $t - c \left (\dfrac {1}{T _{2}} - \dfrac {1}{T _{1}}\right )$

  2. $t = c \left (\dfrac {1}{T _{2}^{2}} - \dfrac {1}{T _{1}^{2}}\right )$

  3. $t = c \left (\dfrac {1}{T _{2}^{3}} - \dfrac {1}{T _{1}^{3}}\right )$

  4. $t = c \left (\dfrac {1}{T _{2}^{4}} - \dfrac {1}{T _{1}^{4}}\right )$

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Correct Option: C

Calculate the surface temperature of the planet, if the energy radiated by unit area in unit time is $5.67 \times 10^4$ watt.

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

  1. $1273^{\circ}C$

  2. $1000^{\circ}C$

  3. $727^{\circ}C$

  4. 727K

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Correct Option: C
Explanation:

According to stefan's Boltzmann law, the energy radiated per unit time:
$E=\sigma A{ T }^{ 4 }$
It is given that: ${E}={5.67}\times{10}^{4}$
Therefore, ${5.67}\times{10}^{4}={5.67}\times{10}^{-8}\times1\times{T}^{4}$
So, ${T}={1000}K$
${T}={1000-273}={727} \  ^oC$

A hot liquid is kept in a big room . the logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. the plot will be very nearly

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

  1. a straight line

  2. a circular arc

  3. a parabola

  4. an ellipse

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Correct Option: A

A solid at temperature $ T _1 $ is kept in an evacuated chamber at Temperature $ T _2 > T _1 $ . the rate of increase of temperature of the body is proportional to

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

  1. $ T _2- T _1 $

  2. $ T^2 _2 - T^2 _1 $

  3. $ T^3 _2 -T^3 _1 $

  4. $ T^4 _1 - T^4 _1 $

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Correct Option: D

A black body radiates energy at the rate of $E$ watt per metr$e^2$ at a high ternperature $T$ K. when the temperature is reduced to $(T/2)$ K, the radiant energy will be

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

  1. $E/16$

  2. $E/4$

  3. $E/2$

  4. $2E$

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Correct Option: A
Explanation:

By Stefan-Boltzmann law black body radiation of energy $E$ is directly proportional to fourth power of $T$ temperature of the black body.
$E\quad \propto \quad { T }^{ 4 }$
If the temperature of the body is reduced to $\dfrac{T}{2}$, the energy of radiation will be $\dfrac{E}{16}$
option (A) is the correct answer.

The rate of radiation of a black body at $0^{\circ}C$ is $E$ J/s. Then the rate of radiation of this black body at $273^{\circ}C$ will be

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

  1. 16 E

  2. 8 E

  3. 4 E

  4. E

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Correct Option: A
Explanation:

From the stefan's law: ${E}={\sigma}{A}{T}^{4}$
So, ${E}={\sigma}{A}{273}^{4}$------(1)
Now, for second one ${E} _{1}={\sigma}{A}{546}^{4}$-----(2)
On dividing equation(2) by (1), we get
$\dfrac{{E} _{1}}{E}=\dfrac{{546}^{4}}{{273}^{4}}={16}$

Or, we can say ${E} _{1}={16}{E}$

The temperature of a spherical planet is related to the distance from sun as :

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

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

  2. $T\propto \dfrac{1}{\sqrt{d}}$

  3. $T\propto d$

  4. $T\propto d^{2}$

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Correct Option: B
Explanation:
A planet reaches its equilibrium temperature when the amount of heat it absorbs from the sun is equal to the amount that it radiates back to space.
The energy absorbed is equal to the insolation at planet's distance (which is Sun's bolometric output divided by $4\pi$ times the distance squared) times the planet's profile area times the planet's Bond aldedo. The amount radiated (assuming that the thermal radiation is approximately black body radiation) is proportional to the planet's surface area times its emmisivity times the forth power of its temperature.

Now, throwing away 2, $\pi$ and other constants that do not vary with temperature or distance.
${ T }^{ 4 }\alpha \cfrac { 1 }{ { d }^{ 2 } } \\ \Rightarrow T\alpha \cfrac { 1 }{ \sqrt { d }  } $

Assertion (A): The radiation from the sun surface varies as the fourth power of its absolute temperature.
Reason (R): Sun is not a black body

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

  1. Both A and R are true, R is correct explanation of A

  2. Both A and R are true, R is not correct explanation of A

  3. A is true but R is false

  4. Both A and R are false

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Correct Option: B
Explanation:

According to Stefan's law, energy emitted is proportional to fourth power of absolute temperature.
So, the same will hold for the sun.
Also, Sun can absorb/emit radiations of all wavelengths - so it is a black body.
So, assertion and reason are both correct.
But reason is not a correct explanation of assertion.
Because all bodies emit energy which is proportional to fourth power of absolute temperature, not only sun.

Three bodies A, B, C are at $-27^{o}$C, $0^{o}$C, $100^{o}$C respectively. The body which does not radiate heat is:

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

  1. A

  2. B

  3. none as all the bodies radiate heat

  4. C

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Correct Option: C
Explanation:

All bodies radiate heat irrespective of temperature.
Heat radiated per unit time is given by Stefan's law.