Tag: thermal properties

Quizzes (8) Questions (112)

Questions Related to thermal properties

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

The temperature of a piece of metal is raised from $27^oC$ to $51.2^oC$. The rate at which the metal radiates energy increases nearly

  1. 1.36 times

  2. 2 times

  3. 4 times

  4. 8 times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rate at which a substance radiates is directly proportional to the fourth power of the absolute temperature.
The temperature increases from $300K$ to $324.2K$ which is an increase by $1.080$
Hence the rate at which the metal radiates would increase by $(1.08)^{4}$ = $1.36$

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

A black body at a temperature $77^oC$ radiates heat at a rate of $10 calcm^{-2}s^{-1}$. The rate at which this body would radiate heat in units of $cal \ cm^{-2} \ s^{-1}$ at $427^oC$ is closest to:

  1. 40

  2. 160

  3. 200

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Energy radiated $P=\sigma AT^4$
$ \displaystyle \frac{P _1}{P _2} = \cfrac{T _1^4}{T _2^4}= { \bigg ( \frac {350}{700} \bigg ) }^4 = \frac{10}{P _2} \space or P _2 = 160$

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

The amount of thermal radiations emitted from one square centimeter area of a black body in a second when at a temperature of 1000K

  1. 5.67 J

  2. 56.7 J

  3. 567 J

  4. 5670 J
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Stefan's law $\Delta Q = \sigma ST^4\Delta t$
$\sigma=5.67E- 8W/m^2K^4;\, S=1E-4m^2;\, T=1000K; \, \Delta t=1s;$
subsutituting value in Stefan's law $\Delta Q=5.67J$
The value can be directly calculated by the Stefan's equation. After substituting the parameters sigma $= 5.67 E-8  W/m^2/K^4, A=10^-4 m^4,$ $T=1000K$ the value comes $5.67$ J
Thus, A is correct answer.
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Find the radiation pressure of solar radiation on the surface of earth. Solar constant is $1.4kW{{m}^{-2}}$

  1. $4.7\times { 10 }^{ -5 }Pa$

  2. $4.7\times { 10 }^{ -6 }Pa$

  3. $2.37\times { 10 }^{ -6 }Pa$

  4. $9.4\times { 10 }^{ -6 }Pa$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
METHOD-1:
${Pressure} _{absorbed}=\dfrac{E _{f}}{c}$
${E} _{f}=$ energy flux, $C=$ Speed of light

${ Pressure } _{ absorbed }=\dfrac { 1.4\times 1000 }{ 3\times { 10 }^{ 8 } } =4.66\times { 10 }^{ -6 }Pa$

METHOD-2: (checking the unit,if formula is not remembered)

We know that:
${Power}={force}\times{velocity}$-----(1)
${Pressure}=\dfrac{force}{area}$------(2)

${Force}=\dfrac{power}{velocity}=\dfrac { 1.4\times 1000 }{ 3\times { 10 }^{ 8 } } =4.66\times { 10 }^{ -6 } newton$

Put in equation (2)
${ Pressure } _{ absorbed }=\dfrac { 4.66\times { 10 }^{ -6 }N }{ { m }^{ 2 } } =4.66\times { 10 }^{ -6 }Pa$
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of a black body corresponding to which it will emit energy at the rate of $1 watt/cm^2$ will be

  1. 650K

  2. 450K

  3. 350K

  4. 250K
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$E\propto { T }^{ 4 }\quad \Longrightarrow \quad E=\sigma { T }^{ 4 }$
$\sigma =5.67*{ 10 }^{ 8 }W{ m }^{ 2 }{ k }^{ 4 }$
$1*{ 10 }^{ -4 }=5.67*{ 10 }^{ 8 }*{ T }^{ 4 }$
$T=648k\cong 650k$



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

The solar constant for the earth is $\Sigma$. The surface temperature of the sun is $T$ K. The sun subtends an angle $\theta$ at the earth

  1. $\Sigma \space \propto \space T^4$

  2. $\Sigma \space \propto \space T^2$

  3. $\Sigma \space \propto \space \theta^4$

  4. $\Sigma \space \propto \space \theta$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By Stephan Boltzman law,


$P=\sigma (4\pi { R }^{ 2 }){ T }^{ 4 }$

$\theta =\dfrac { 2r }{ R } $ where R is distance between earth and sun and r is radius of earth.

Hence, $\sum {  } =\dfrac { P }{ 4\pi { r }^{ 2 } } =C{ T }^{ 4 }{ \left( \dfrac { R }{ r }  \right)  }^{ 2 }=K{ T }^{ 4 }{ \theta  }^{ 2 }$

Hence $\sum {  } \alpha { T }^{ 4 }$ and $\sum {  } \alpha { \theta }^{ 2 }$

Answer is option A.

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

In the Orion stellar system the shining of a star is $17\space \times 10^3$ times that of the sun. If the temperature of the surface of the sun $6 \times 10^3 K$ then the temperature of this star will be

  1. 273 K

  2. 652 K

  3. 6520 K

  4. 68520 K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The power radiated is directly proportional to the fourth power of the absolute temperature.
$P \propto T^{4}$
$P = kT^{4}$ 

Let P = Power radiated by the sun
Power radiated by star $ = 17 \times  10^{3}P $
$\dfrac{T _{star}^{4}}{T _{sun}^{4}} = 17 \times  10^{3}$

$\dfrac{T _{star}}{T _{sun}} = 11.418$

$T _{star} = 6000 \times  11.418 = 68,511K$

Hence, the answer is option D.

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

There are two planets $A$ and $B$ at a large distance Planet $A$ is bigger and hotter than planet $B$. The angular diameter of planet $A$ is $40$ minute of arc as seen from planet $B$. The energy received by planet $B$ is $3cal-cm^{-2}$ per minute. Assuming the radiation to be black body in character. Given that stefan costant is $5.67\times 10^{-8}\ Wm^{-2}\ K^{-4}$. The temperature of planet $A$ is

  1. $(10.93\times 10^{14})^{1/4}\ K$

  2. $(53.21\times 10^{14})^{1/4}\ K$

  3. $(63.63\times 10^{14})^{1/4}\ K$

  4. $(63.21\times 10^{14})^{1/4}\ K$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The energy received by planet B is given by the Stefan-Boltzmann law applied to the radiation from A reaching B. Using the angular diameter and the flux, one can determine the temperature of A.

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.