Tag: heat and thermodynamics

Questions Related to heat and thermodynamics

The temperature of the black body that radiates heat at a rate of $459.27 \times 10^4 W m^{-2}$ is:

laws of heat transfer heat and thermodynamics physics

  1. 1000K

  2. 2000K

  3. 3000K

  4. 4000K

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Correct Option: B

Which one of the following is the characteristic of Planck's quantum theory of radiation?

laws of heat transfer heat and thermodynamics physics

  1. The energy is not absorbed or emitted in integral multiple of quantum of energy.

  2. Radiation energy is not emitted or absorbed continuously but in the form of small packets of energy

  3. Radiation energy is emitted or absorbed continuously

  4. The magnitude of energy associated with a quantum is inversely proportional to its frequency

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Correct Option: B
Explanation:

According to Planck's quantum theory, radiation is emitted in the form of small packets of energy and is not continuous. Quantum of energy can be expressed by the relation E=hv, where h is Planck's constant and v is the frequency.

Pervost's theory of heat exchange is not applicable at temperature

laws of heat transfer heat and thermodynamics physics

  1. $0^oR$

  2. $0^oC$

  3. $0 K$

  4. $0^oF$

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Correct Option: C
Explanation:

Prevost postulated that  radiative equilibrium is the condition where a steady state system is in dynamic equilibrium, with equal incoming and outgoing radiative flux and negligible heat transfer by conduction and convection.
So by extended logic, at $0K$ equilibrium cannot be reached.

Two spheres made of same material have radii in the ratio 2 : 1. If both the spheres are at same temperature, then what is the ratio of heat radiation energy emitted per second by them?

laws of heat transfer heat and thermodynamics physics

  1. 1 : 4

  2. 4 : 1

  3. 3 : 4

  4. 4 : 3

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Correct Option: B
Explanation:

Radiation emitted per second depends on the temperature of the body.
Stefan's law states that the rate of emission of radiant energy by unit area of perfectly black body is directly proportional to the fourth power of its absolute temperature.
      $E \propto AT^4$
or   $E \propto r^2$
($\because A= \pi r^2$ and T is same for both the spheres)
where r is radius of sphere.
$\frac{E _1}{E _2} = \frac{r^2 _1}{r^2 _2}$
$=\left(\frac{2}{1}\right)^2=\frac{4}{1}$
$=4:1$
Note : A black body at absolute temperature T surrounded by another black body at absolute temperature $T _0$ not only loses an amount of energy $\sigma T^4$, thus the amount of heat lost by the former per unit time is given by 
$E=\sigma (T^4-T _0^4)$
This law is stefan Boltzmann's law.

A temperature of a body is ${400^ \circ }$ C. Assuming the surrounding temperature to be negligible. At what temperature will body emit double energy radiation?

laws of heat transfer heat and thermodynamics physics

  1. ${200^ \circ }$ c

  2. 200 K

  3. ${800^ \circ }$ c

  4. 800 K

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Correct Option: D

If the temperature of a hot body is increased by $50\%$, then the increase in the quality of emitted heat radiation will be

laws of heat transfer heat and thermodynamics physics

  1. $125\%$

  2. $200\%$

  3. $300\%$

  4. $400\%$

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Correct Option: B

If the operating voltage of X-ray tube is $50$kV then velocity of X-ray?

laws of heat transfer heat and thermodynamics physics

  1. $7.5\times10^{25}$ m/sec

  2. $3\times 10^8$ m/sec

  3. $10^8$ m/sec

  4. $3$ m/sec

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Correct Option: A
Explanation:

We know, wavelength of X-ray $\lambda =\dfrac { hv }{ eV } $

Where h is the Plank's constant and $v$ is the required velocity.
$v=\frac { \lambda \times eV }{ h } $
  the minimum wavelength of X-ray is 0.01 nm.
So velocity, $\ \quad \quad v=\frac { 0.01\times { 10 }^{ -9 }\times 50\times { 10 }^{ 3 } }{ 6.626\times { 10 }^{ -34 } } $
     v= $0.0754\times { 10 }^{ 28 }\quad m/s\ =7.5\times { 10 }^{ 25 }\quad m/s$


The hydrogen atom in its ground state is excited by means of monochromatic radiation of energy $12.75ev$. How many different lines are possible in the resulting spectrum? You may assume the ionization energy for hydrogen atom as $13.6\ eV$

laws of heat transfer heat and thermodynamics physics

  1. $3$

  2. $4$

  3. $6$

  4. $2$

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Correct Option: B

If $c$ is the velocity of electromagnetic radiation $e$ is the charge of an electron $m$ is the mass of an electron and $h$ is the Planck's constant, then the combination of these universal constant that is dimensionless, is

laws of heat transfer heat and thermodynamics physics

  1. $me^{2}/(hc)$

  2. $hc/(me)$

  3. $mc^{2}/h$

  4. $None$

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Correct Option: D

The radiation corresponding to 3 $\rightarrow $ s 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 10 ^ { - 4 } T$ . If the radius of the largest circular path followed by these electrons is 100 mm, the work function of the metal is close to 

laws of heat transfer heat and thermodynamics physics

  1. 3.8 eV

  2. 1.1 eV

  3. 1.8 eV

  4. 1.6 eV

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Correct Option: B
Explanation:

$mv=qBR$

$K{E _{\max }} = \dfrac{{\left( {m{v^2}} \right)}}{{2m}} = 0.8\,eV$
$hv = 13.6\left[ {\dfrac{1}{4} - \dfrac{1}{6}} \right]$
$\therefore W = hv - K{E _{\max }}$
$ = 13.6 \times \dfrac{5}{{36}} - 0.8 = 1.1eV$
Hence,
option $(B)$ is correct answer.