Physics

Thermal Properties and Thermodynamics

380 Questions

Thermal properties and thermodynamics questions evaluate concepts of heat transfer, thermal efficiency, and temperature variations. Problems involve calculating heat content, conductivity, and the performance of heat engines. This subject is regularly tested in physics sections across multiple competitive platforms.

Heat transfer calculationsThermal efficiencyBlack body radiationTemperature variationsRefrigeration performance

Thermal Properties and Thermodynamics Questions

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

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.

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

A solid shpere and a hollow sphere of the same material and of equal radii are heated to the same temperature

  1. both will emit equal amount of radiation per unit time in the beginning.

  2. both will absorbs equal amount of radiation per second from the surrounding in the beginning.

  3. the initial rate of cooling will be the same for both the spheres

  4. the two spheres will have equal temperature at any instant
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

According to many radiation laws like Stefan Boltzmann we know that radiation emission and absorption are a purely surface phenomenon. Since the two bodies are of same material, same radii, and same temperature they will at that instant radiate and absorb at the same rates.
But however since the hollow sphere has lesser mass, the rate at which it's temperature will rise will be different from that of the solid sphere. Hence their rates of cooling would be varied and they would have different temperatures at different times.

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

A black body at 127$^{o}$C emits the energy at the rate of 10$^{6}$ J/m$^{2}$ s. The temperature of a black body at which the rate of energy emission is 16x10$^{6}$ J/m$^{2}$ s is :

  1. $508^{o}C$
  2. $273^{o}C$
  3. $400^{o}C$
  4. $527^{o}C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using Stefan's Law:
$\dfrac { { E } _{ 2 } }{ { E } _{ 1 } } ={ \left( \dfrac { { T } _{ 2 } }{ { T } _{ 1 } }  \right)  }^{ 4 }\ { T } _{ 2 }={ T } _{ 1 }\sqrt [ 4 ]{ \dfrac { { E } _{ 2 } }{ { E } _{ 1 } }  } \quad \ { T } _{ 2 }={ (127+273) }\sqrt [ 4 ]{ \dfrac { 16\times { 10 }^{ 6 } }{ { 10 }^{ 6 } }  } =\quad 800K\ { T } _{ 2 }={ 527 }^{ \circ  }C$

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 of 2T and 3T respectively. The temperatures of the middle (i.e. second) plate under steady state condition is then

  1. $\left ( \dfrac{64}{2} \right )^{\dfrac{1}{4}}T$
  2. $\left ( \dfrac{97}{4} \right )^{\dfrac{1}{4}}T$
  3. $\left ( \dfrac{97}{2} \right )^{\dfrac{1}{4}}T$
  4. $\left ( 97\right )^{\dfrac{1}{4}}T$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is identical to question 534600. The steady state temperature of the middle plate is ( (T1^4 + T3^4) / 2 )^(1/4). With T1=2T and T3=3T, T2 = ((16T^4 + 81T^4)/2)^(1/4) = (97/2)^(1/4) * T.

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

The rectangular surface of area $8cm$ $\times$ $4 cm$ of a black body at temperature $127^{\circ}C$ emits energy $E$ per second. If the length and breadth are reduced to half of the initial value and the temperature is raised to $327^{\circ}C$, the rate of emission of energy becomes

  1. $\displaystyle \frac{3}{8}E$
  2. $\displaystyle \frac{81}{16}E$
  3. $\displaystyle \frac{9}{16}E$
  4. $\displaystyle \frac{81}{64}E$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By $Stefan's$ Law

$Power=\sigma A T^4$
$A=length\times breadth$
$\dfrac{P _2}{E}=\dfrac{l _2b _2T _2^4}{l _1b _1T _1^4}$
Here$\dfrac{l _2}{l _1}=\dfrac{1}{2}$       $\dfrac{b _2}{b _1}=\dfrac{1}{2}$       $\dfrac{T _2}{T _1}=\dfrac{3}{2}$

$\implies P _2=\dfrac{81}{64}E$

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

If the temperature of a hot body is raised by $0.5\%$, then the heat energy radiated would increase by :

  1. 0.5%

  2. 1.0%

  3. 1.5%

  4. 2.0%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The rate of heat energy radiated by black body is given as:
$Q=\sigma T^4A$ where $\sigma$ is the stefen-boltzmann constant, $A$ is the area of the radiating body.
So $Q\propto T^4=kT^4$, where $k$ is the propotionality constant that we have assumed here.
Taking log of above equation, $logQ=log(kT^4)=logk+4logT$
Taking differential of above equation, $\dfrac{dQ}{Q}=0+\dfrac{4dT}{T}$ (because logk is constant).
Here $dQ$ and $dT$ indicate very small change in the $Q$ and $T$ respectively.
Multiplying by $100$,
$\dfrac{dQ}{Q}\times100=4\dfrac{dT}{T}\times100$
$\Rightarrow$ Percentage change in Heat rate $=4\times $ percentage change in temperature
So here, percentage change in rate of heat energy radiated $=4\times0.5=2\%$
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of a black body is increased by $50\%$ . Then the percentage of increase of radiation is approximately

  1. 100%

  2. 25%

  3. 400%

  4. 500%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By $Stefan's$ $Law$,

Power = ${\sigma A {T}^{4}}$ for a black body
$\sigma$ is known as Stefan's constant
$\dfrac{P _1}{P _2}$ = $\dfrac{ T _1^4}{ T _2^4}$
${T _2}$ = $\dfrac{3 T _1}{2}$
$\dfrac{T _1^4}{T _2^4}$= $\dfrac{16}{81}$
By the above equations we get
$P _2$=$\dfrac{81 P _1}{16}$
Percentage increase in radiation = $\dfrac{P _2 - P _1}{P _1}$ x $100$ = $406.25$%

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

The rays of sun are focussed on a piece of ice through a lens of diameter $5$ cm, as a result of which $10$ grams of ice melts in $10$ min. The amount of heat received from Sun is (per unit area per min)

  1. 4 $cal/cm^{2} \: min$
  2. 40 $cal/cm^{2} \: min$
  3. 4 $J/cm^{2} \: min$
  4. 400 $J/cm^{2} \: min$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The latent heat of fusion is $80cal/g$.

So heat received per unit times is $10g\times 80cal g^{-1}/ 10min=80cal/min$
The are is $\pi r^2=\pi\times(2.5)^2cm^2\approx 20cm^2$
So, amountof heat per unit area per unit time is $80/20=4cal/cm^2\ min$

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

Which of the following statements is true/correct?

  1. During clear nights, the temperature rises steadily upward near the ground level

  2. Newton's law of cooling, and approximate form of Stefan's law, is valid only for natural convection

  3. The total energy emitted by a black body per unit time per unit area is proportional to the square of its temperature in the Kelvin scale
  4. Two spheres of the same material have radii $1 m$ and $4 m$ and temperatures $4000 K$ and $2000 K$ respectively. The energy radiated per second by the first sphere is greater than that radiated per second by the second sphere
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

During clear nights object on surface of earth radiate out heat and temperature falls. Hence option (a) is wrong.
The total energy radiated by a body per unit time per unit area $E \propto {T}^{4}$. Hence option (c) is wrong.
Energy radiated per second is given by
$\dfrac { Q }{ t } =PA\varepsilon \sigma { T }^{ 4 }$
$\Rightarrow \dfrac { { P } _{ 1 } }{ { P } _{ 2 } } =\dfrac { { A } _{ 1 } }{ { A } _{ 2 } } { \left( \dfrac { { T } _{ 1 } }{ { T } _{ 2 } }  \right)  }^{ 4 }={ \left( \dfrac { { r } _{ 1 } }{ { r } _{ 2 } }  \right)  }^{ 2 }\cdot { \left( \dfrac { { T } _{ 1 } }{ { T } _{ 2 } }  \right)  }^{ 2 }$
$={ \left( \dfrac { 1 }{ 4 }  \right)  }^{ 2 }\left( \dfrac { 4000 }{ 200 }  \right) =\dfrac { 1 }{ 1 } $
$\because    {P} _{1} = {P} _{2}$ hence option (d) is wrong.
Newton's law is an approximate from of Stefan's law of radiation and works well for natural convection. Hence option (b) is correct.