Physics

Thermal Properties and Thermodynamics

431 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 physics energy production perfectly black body black-body radiation black body radiation

Initially a black body at absolute temperature $T$ is kept inside a closed chamber at absolute temperature $T _{o}$. Now the chamber is slightly opened to allow sun rays to enter. It is observed that temperatures $T$ and $T _{o}$ remains constant.Which of the following statement is/are true?

  1. The rate of emission of energy from the black body remains the same

  2. The rate of emission of energy from the black body increases

  3. The rate of absorption of energy by the black body increases.

  4. The energy radiated by the black body equals the energy absorbed by it
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

It is given that the absolute temperatures of both the black body and the surroundings are constant with time, even after sunlight(radiation) is incident on it.

  • When a body absorbs radiation, its temperature increases
  • When a body emits radiation, its temperature decreases
Also the sun, being a source of infinite radiation(very large source of radiation).
We infer from this that the incident radiation should be of constant magnitude.
And if the temperature of the black body is a constant, that means it's emission and absorption of radiation are matched and equal. The absorption is of constant magnitude, because the sun's radiation is of constant value. Hence the emission is of constant value also and is equal to the absorption. The options follow.

Multiple choice physics energy production perfectly black body black-body radiation black body radiation

A spherical body of area A and emissivity $e = 0.6$ is kept inside a perfectly black body. Total heat radiated by the body at temperature $T$ 

  1. $ 0.8\ e\sigma AT^4$
  2. $ 0.4\ e\sigma AT^4$
  3. $ 0.6\ e\sigma AT^4$
  4. $ 1.0\ e\sigma AT^4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
According to Stefan's Boltzman law, the thermal energy radiated by a black body radiator per second per unit area is proportional to fourth power of the absolute temperature and is given by
$\dfrac{P}{A} = \sigma T^4$ ..............(1)
For the hot bodies other than black body radiator equation (1) becomes,
$\dfrac{P}{A} = e \sigma T^4$
$P = e \sigma A T^4$ .................(2)
where, $e$ is the emissivity of the body.
Now, when such hot body is kept inside a perfectly black body, the total thermal radiation is the sum of emitted radiations (in open) and the part of incident radiations reflected from the walls of the perfectly black body. This will give black body radiations, hence the total radiations emitted by the body will be,
$P = 1.0 e \sigma A T^4$.
Multiple choice physics energy production perfectly black body black-body radiation black body radiation

Emissivity of a perfect black body is

  1. always $0$.
  2. always $1$.
  3. between $0$ and $1$.
  4. always $>1$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Emissivity of a perfect black body is always 1.
The best absorber is defined as the object which can absorb all the electromagnetic radiations falling upon it. The black body is not only a perfect absorber but it is also the best in emitting radiation. Also, a black bosy in thermal equlibrium has emissivity, $\epsilon=1$
Multiple choice physics energy production perfectly black body black-body radiation black body radiation

The Wien's displacement law for a black body is
($T$ is the absolute temperature in $K$
$b$ is a constant of proportionality 
$e$ is the emissivity of the black body)

  1. $\lambda _{max} T = b$
  2. $\lambda _{max} T = e$
  3. $\lambda _{max} b = T$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
According to wein's displacement law there is inverse relation between $\lambda _{max}$ of radiation emitted by black body and its temperature (absolute)
$\lambda _{max}\; \alpha \; \cfrac{1}{T} \Rightarrow =b\cfrac{1}{T} \Rightarrow \lambda _{max} T=b$
Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

If temperature of body increases by 10%, then increase in radiated energy of the body is :

  1. 10 %

  2. 40 %

  3. 46 %

  4. 1000 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Stefan-Boltzmann law, radiated energy E is proportional to T^4. If T increases by 10%, T_new = 1.1T. Then E_new = (1.1)^4 * E = 1.4641 * E. The increase is 46.41%.

Multiple choice physics behaviour of perfect gas and kinetic theory of gases degree of freedom: law of equipartition of energy law of equipartition of energy law of equipartition of energy and mean free path

To find out degree of freedom, the correct expression is :

  1. $f=\dfrac { 2 }{ \gamma -1 }$
  2. $f=\dfrac { \gamma +1 }{ 2 }$
  3. $f=\dfrac { 2 }{ \gamma +1 }$
  4. $f=\dfrac { 1 }{ \gamma +1 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\because \gamma =1+\dfrac { 2 }{ f } $
$\Longrightarrow \dfrac { 2 }{ f } =\gamma -1\Longrightarrow f=\dfrac { 2 }{ \gamma -1 } $

Multiple choice rotational equilibrium option b: engineering physics motion of system of particles and rigid bodies equilibrium physics

Three copper blocks of masses ${ M } _{ 1 }$, ${ M } _{ 2 }$, and ${ M } _{ 3 }$, kg respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at ${ T } _{ 1 }$,${ T } _{ 2 }$,${ T } _{ 3 }$ $\left( { T } _{ 1 }{ >T } _{ 2 }>{ T } _{ 3 } \right)$. Assuming there is no heat loss to the surroundings, the equilibrium temperature T is (s is specific heat of copper)     

  1. $T=\dfrac { { T } _{ 1 }{ +T } _{ 2 }+{ T } _{ 3 } }{ 3 } $
  2. $T=\dfrac { { { { M } _{ 1 }T } _{ 1 }{ +{ M } _{ 2 }T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } } }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } } $
  3. $T=\dfrac { { { M } _{ 1 }T } _{ 1 }{ +{ M } _{ 2 }T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } }{ 3\left( { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } \right) } $
  4. $T=\dfrac { { { M } _{ 1 }T } _{ 1 }s{ +{ M } _{ 2 }T } _{ 2 }s+{ M } _{ 3 }{ T } _{ 3 }s }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let us assume that $T _1>T _2,T _3$ and $T _1>T>T _2,T _3$

Now heat loss by $M _1=$ Heat gained by $M _2$ and $M _3$

$M _1S(T _1-T)=M _2S(T-T _1)+M _3S(T-T _3)$

$\implies M _1T _1+M _2T _2+M _3T _3=(M _1+M _2+M _3)T$

$\implies T=\dfrac{M _1T _1+M _2T _2+M _3T _3}{M _1+M _2+M _3}$
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A heated body emits radiation which has maximum intensity at frequency $v _m$. If the temperature of the body is doubled

  1. the maximum intensity radiation will be at frequency $2v _m$
  2. the maximum intensity radiation will be at frequency $\displaystyle\dfrac{1}{2}v _m$
  3. the total emitted energy will increase by a factor of $16$
  4. the total emitted energy will increase by a factor of $2$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Wien's displacement law states maximum intensity wavength $ \lambda _{m}\propto \dfrac{1}{T}$
Also for any photon,$ \lambda \propto \dfrac{1}{\nu}$
Hence, frequency $\nu _m \propto T$
Doubling of temperature leads to doubling of frequency from $\nu _m$ to $ 2\nu _m$
From Stefan's law, power is directly proportional to $T^4$
Hence $ T \rightarrow 2T \Rightarrow E \rightarrow (\dfrac {2T}{T})^4E=16E$

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

  1. $(\cfrac{65}{2})^{\frac{1}{4}}T$
  2. $(\cfrac{97}{4})^{\frac{1}{4}}T$
  3. $(\cfrac{97}{2})^{\frac{1}{4}}T$
  4. $(97)^{\frac{1}{4}}T$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In steady state, the heat flux through each gap between the plates must be equal. Using the Stefan-Boltzmann law for radiative heat transfer between parallel plates, the heat flux q = sigma * (T1^4 - T2^4). Setting the flux between plate 1 and 2 equal to the flux between plate 2 and 3, we get (2T)^4 - T2^4 = T2^4 - (3T)^4. Solving for T2 gives T2 = ((2^4 + 3^4)/2)^(1/4) * T = (97/2)^(1/4) * T.

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

The energy emitted by a black body at $727^oC$ is E. If the temperature of the body is increased by $227^oC$, the emitted energy will become

  1. 13 times

  2. 2.27 times

  3. 1.9 times

  4. 3.9 times
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here we know that energy emitted by any body is given by ${E}=\sigma{T^{4}}$

So, at temperature ${T}={727}^{o}C$ energy emitted will be ${E}$
at temperature ${T} _{1}={727+227}={954}^{o}C$ energy emitted will be ${E} _{1}={\sigma}{T} _{1}^{4}$
$\dfrac { E }{ { E } _{ 1 } } =\dfrac { { T }^{ 4 } }{ { T } _{ 1 }^{ 4 } }$
${ E } _{ 1 }=\dfrac { E\times { T } _{ 1 }^{ 4 } }{ { T }^{ 4 } } =\dfrac { E\times { 954 }^{ 4 } }{ { 727 }^{ 4 } } =2.96E$

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

In pyrometer , temperature measured is proportional to $\underline{\hspace{0.5in}}$ energy emitted by the body 

  1. light

  2. electric

  3. radiation

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

Stefan- Boltzann law, $j^{ \star  }=\varepsilon \sigma T^{ 4 }$ connects temperature T with thermal radiation or irradiance  $j^{ \star  }$.
Thus measuring the irradiance with pyrometer yields the temperature of the body.

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

Two bodies of same shape and having emissivities 0.1 and 0.9 respectively radiate same energy per second. The ratio of their temperature is :

  1. $\sqrt{3}:1$
  2. $1:\sqrt{3}$
  3. $3:1$
  4. $1:3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\dfrac{E}{t}=e \sigma A T^4$
From above equation which is Stefan's Law of radiation, it is clear that:
$\dfrac{E _1}{E _2} = \dfrac{{e} _{1}\sigma{T} _{1}^{4}}{{e} _{2}\sigma{T} _{2}^{4}}$

$1 = \dfrac{{0.1}{T} _{1}^{4}}{{0.9}{T} _{2}^{4}}$

$\dfrac{{T} _{1}}{{T} _{2}} = \dfrac{\sqrt{3}}{1} $
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Two bodies A and B are kept in an evacuated chamber at $27^oC$. The temperature of A and B are $327^oC$ and $427^oC$ respectively. The ratio of rate of loss of heat from A and B will be

  1. 0.25

  2. 0.52

  3. 1.52

  4. 2.52
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The power radiated is directly proportional to fourth power of absolute temperature.
i.e.
$P \propto T^{4}$
$\frac{P _{1}}{P _{2}} = (\frac{T _{1}}{T _{2}})^{4}$
$\frac{P _{1}}{P _{2}} = (\frac{327+273}{427+273})^{4} = 0.53$
Hence the ratio of rate of heat loss = 0.53
Hence option B is correct.

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

The thermal radiation emitted by a body is proportional to $T^{n}$ where $T$ is its absolute temperature. The value of $n$ is exactly $4$ for

  1. a blackbody

  2. all bodies

  3. bodies painted balck only

  4. polished bodies only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By Stefan's Law, rate of thermal radiation is directly proportional to fourth power of temperature of the body.
$Q = \sigma {T}^{4}$