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 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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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.

  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. $t = c \left (\dfrac {1}{T _{2}^{4}} - \dfrac {1}{T _{1}^{4}}\right )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Stefan-Boltzmann law, the rate of cooling is dQ/dt = -sigma * A * T^4. Since dQ = mc * dT, we have mc * dT/dt = -sigma * A * T^4. Separating variables, T^-4 * dT = -(sigma * A / mc) * dt. Integrating gives (1/3) * T^-3 = (sigma * A / mc) * t. Thus t is proportional to (1/T2^3 - 1/T1^3).

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

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

  1. $1273^{\circ}C$

  2. $1000^{\circ}C$

  3. $727^{\circ}C$

  4. 727K
Reveal answer Fill a bubble to check yourself
C Correct answer
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, ${T}={1000}K$
${T}={1000-273}={727} \  ^oC$

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

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

  1. a straight line

  2. a circular arc

  3. a parabola

  4. an ellipse
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Newton's law of cooling, dT/dt = -k(T - T_room). Integrating this gives ln(T - T_room) = -kt + C. Thus, the plot of the logarithm of the temperature difference versus time is a straight line.

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

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

  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 $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rate of heat exchange for a body at temperature T1 in a chamber at T2 is proportional to the difference in the fourth powers of the temperatures (T2^4 - T1^4) due to radiative heat transfer.

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

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

  1. $E/16$

  2. $E/4$

  3. $E/2$

  4. $2E$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. 16 E

  2. 8 E

  3. 4 E

  4. E
Reveal answer Fill a bubble to check yourself
A Correct answer
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 ${E} _{1}={16}{E}$

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

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

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

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

  3. $T\propto d$

  4. $T\propto d^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 }  } $
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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:

  1. A

  2. B

  3. none as all the bodies radiate heat

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

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