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Laws of heat transfer - class-XI online quiz

Description: Heat and thermodynamics
Number of Questions: 18
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Tags: heat and thermodynamics physics
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The temperature of the black body that radiates heat at a rate of $459.27 \times 10^4 W m^{-2}$ is:

  1. 1000K

  2. 2000K

  3. 3000K

  4. 4000K


Correct Option: B

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

  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


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

  1. $0^oR$

  2. $0^oC$

  3. $0 K$

  4. $0^oF$


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?

  1. 1 : 4

  2. 4 : 1

  3. 3 : 4

  4. 4 : 3


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?

  1. ${200^ \circ }$ c

  2. 200 K

  3. ${800^ \circ }$ c

  4. 800 K


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

  1. $125\%$

  2. $200\%$

  3. $300\%$

  4. $400\%$


Correct Option: B

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

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

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

  3. $10^8$ m/sec

  4. $3$ m/sec


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 $13.6\ eV$

  1. $3$

  2. $4$

  3. $6$

  4. $2$


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

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

  2. $hc/(me)$

  3. $mc^{2}/h$

  4. $None$


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 

  1. 3.8 eV

  2. 1.1 eV

  3. 1.8 eV

  4. 1.6 eV


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.

Two black metallic spheres of radius 4m, at 2000 K and 1m at 4000 K will have ratio of energy radiation as

  1. 1 : 1

  2. 4 : 1

  3. 1 : 4

  4. 2 : 1


Correct Option: A

Two sphere of same material and of same emissivity have radii 1 m and 4 m and temperature 4000 K and 1000 K, respectively. The ratio of radiation emitted per sec is  

  1. 4:1

  2. 1:4

  3. 1:1

  4. 16:1


Correct Option: C

We find that the temperature of air decreases as one goes up from the earth's surface because

  1. The atmospheric pressure drops with height

  2. The earth which radiates in the infrared region is the main heat source and temperature drops as we go away from it

  3. The density of air drops with height and the air therefore cannot hold stronger as we go up

  4. Winds are stronger as we go up


Correct Option: B
Explanation:
The behaviour of atmosphere is different for visible and infrared radiations. Most of the infrared radiations are not allowed to pass through atmosphere, since it reflects them. The energy from the sun, heats the earth which in turn starts emitting radiations. Since, the earth gets heated to much lower temperature than the temperature of the sun, according to Planck's law, the radiations emitted by the earth are mostly in the infrared region. These radiations from the earth are not allowed to pass through the atmosphere which reflects them back. As a result of it the earth's atmosphere becomes richer in infrared radiations which are sometimes called heat radiations. So, earth radiates in the infrared region, this is the source of heat. As we go up, it decreases.

Choose the correct answer from the alternatives given.
Radiations of intensity $0.5\ W/m^2$ are striking a metal plate. The pressure on the plate is then

  1. $0.166 \, \times \, 10^{-8} \, N \, m^{-2}$

  2. $0.332 \, \times \, 10^{-8} \, N \, m^{-2}$

  3. $0.111 \, \times \, 10^{-8} \, N \, m^{-2}$

  4. $0.083 \, \times \, 10^{-8} \, N \, m^{-2}$


Correct Option: A
Explanation:

Given: The intensity of the incident radiations is $0.5\ W/m^2$.


To find: The radiation pressure on the plate.

The radiation pressure experienced by the plate is given as;
$P = \dfrac{I}{c}\\Rightarrow \dfrac{0.5}{3 \times 10^8}\\Rightarrow  0.166 \times 10^{-8} N m^{-2}$

Option $(A)$ is correct.

A pan filled with hot food cools from $94^oC$ to $86^oC$ in$2$ minutes when the room temperature is at $20^oC$. The time taken to cool it from $71^oC$ to $69^oC$ is 

  1. $12\,s$

  2. $22\,s$

  3. $32\,s$

  4. $42\,s$


Correct Option: D
Explanation:

For approximate calculation of the time taken,

$\cfrac { { T } _{ i }-{ T } _{ f } }{ \Delta t } =k\left[ \cfrac { { T } _{ i }+{ T } _{ f } }{ 2 } -{ T } _{ o } \right] $
where,
${ T } _{ o }\longrightarrow $room temperature
$T _{i} \longrightarrow$initial temperature
$T _{f} \longrightarrow$final temperature
$\Delta t \longrightarrow$time taken
$k \longrightarrow$constant
$\Longrightarrow \cfrac { 94-86 }{ 2 } =k\left[ \cfrac { 94+86 }{ 2 } -20 \right] \ \Longrightarrow 4=k[90-20]=k[70]\ \therefore k=\cfrac { 4 }{ 70 } \ \Longrightarrow \cfrac { 71-69 }{ \Delta t } =\cfrac { 4 }{ 70 } \left[ \cfrac { 71+69 }{ 2 } -20 \right] \ \Longrightarrow \cfrac { 2 }{ \Delta t } =\cfrac { 4 }{ 70 } \left[ 70-20 \right] \ \Longrightarrow \cfrac { 2 }{ \Delta t } =\cfrac { 4 }{ 70 } \times 50\ \therefore \Delta t=\cfrac { 70 }{ 2\times 50 } =0.7min=42sec$

Five kilomoles of oxygen is heated at constant pressure. The temperature of the oxygen gas is increased from 295 K to 305 K. If the molar heat capacity of oxygen at  constant pressure is 6.994 kcal/kmole K. The amount of heat absorbed is in kcal,

  1. 249.7

  2. 44

  3. 349.7

  4. 539.7


Correct Option: C

Water is used to cool radiators of engines, because:

  1. Of its lower density

  2. It is easily available

  3. It is cheap

  4. It has high specific heat


Correct Option: D

Star A emits radiation of maximum intensity at a wavelength of $5000 \mathring{A}$ and it has temperature $ 1227^oC $. If star B has temperature $ 2727^oC $ , then the maximum intensity would be observed at 

  1. $ 4000 \mathring{A} $

  2. $ 2250 \mathring{A} $

  3. $ 3000 \mathring{A} $

  4. $ 2500 \mathring{A} $


Correct Option: D
Explanation:

$\begin{array}{l} \dfrac { { \lambda { m^{ 1 } } } }{ { \lambda m } } =\dfrac { T }{ { { T^{ 1 } } } }  \ \dfrac { { \lambda { m^{ 1 } } } }{ { 5000A } } =\dfrac { { 1227+273k } }{ { 2727+273k } }  \ \lambda { m^{ 1 } }=2500A \end{array}$

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