Tag: black body radiation

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Questions Related to black body radiation

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

A blackened steel plate is put in a dark room after being heated up to a high temperature. A white spot on the plate appears. 

  1. brighter than the plate

  2. as bright as the plate

  3. dull as compared to the plate

  4. appears to be yellow
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Kirchhoff's law of radiation, good absorbers are good emitters. A white spot (which is a poor absorber/emitter compared to the blackened surface) will emit less radiation at the same temperature, making it appear darker or less bright than the surrounding blackened surface.

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

Boltzmann's constant$ K = 1.38 \times 10^{-23} J/k $ The energy associated with helium atom the surface of sun, where surface temperature is 6000 K is

  1. $ 1.242 \times 10^{-19} J $

  2. $ 2.484 \times 10^{-19} J $

  3. $ 207 \times 10^{-19} J $

  4. $ 0.621 \times 10^{-19} J $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average kinetic energy of a gas molecule is (3/2)kT. For a helium atom (monatomic), the energy is (3/2) * 1.38 * 10^-23 * 6000 = 1.5 * 1.38 * 6 * 10^-20 = 1.242 * 10^-19 J.

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

If in an ideal gas $r$ is radius of molecule, $P$ is pressure, $T$ is absolute temperature and $k$ is Boltzmann's constant, then mean free path $\overline { \lambda  } $ of gas molecules is given as

  1. $\dfrac { 4\pi \sqrt { 2 } PT }{ k{ r }^{ 2 } } $

  2. $\dfrac { 4\pi \sqrt { 2 } kT }{ P{ r }^{ 2 } } $

  3. $\dfrac { kP }{ 4\pi \sqrt { 2 } { r }^{ 2 }T } $

  4. $\dfrac { kT }{ 4\pi \sqrt { 2 } { r }^{ 2 }P } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The mean free path formula is lambda = kT / (sqrt(2) * pi * d^2 * P). Since the radius r = d/2, d = 2r, so d^2 = 4r^2. Substituting this gives lambda = kT / (4 * sqrt(2) * pi * r^2 * P).

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

Solar constant for earth is $2 \mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 } ,$ if distance ofmerary from sun is 0.4 times than distance of earthfrom sun then solar constant for mercury will be? 

  1. 12.5$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$

  2. 25$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$

  3. 0.32$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$

  4. 2$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The solar energy incident on the roof in 1 hour of dimension $ 8m \times 20m$ will be

  1. $5.76\times { 10 }^{ 8 }J$

  2. $5.76\times { 10 }^{ 7 }J$

  3. $5.76\times { 10 }^{ 6 }J$

  4. $5.76\times { 10 }^{ 5 }J$
Reveal answer Fill a bubble to check yourself
A 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 $=10^3\times (8\times 20)=1.6\times 10^5 W$ 
Since power is the energy divided by time so, energy, $E=Pt=1.6\times 10^5 \times (3600)=5.76\times 10^8  J$

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.