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Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Energy radiated E is proportional to T^4. If E' = 2E, then (T'/T)^4 = 2, so T' = T * 2^(1/4). T = 400 + 273 = 673 K. T' = 673 * 1.189 = 800 K. Converting back to Celsius is not required as the options provide Kelvin.

Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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= $0.0754\times { 10 }^{ 28 }\quad m/s\ =7.5\times { 10 }^{ 25 }\quad m/s$


Multiple choice laws of heat transfer heat and thermodynamics physics

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. $2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice laws of heat transfer heat and thermodynamics physics

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. $None$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The fine structure constant alpha = e^2 / (4 * pi * epsilon_0 * h_bar * c) is dimensionless. The expression me^2 / (hc) is related to the Rydberg energy and is not dimensionless. None of the provided options are dimensionless.

Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Power P = sigma * A * T^4. P1 = sigma * 4 * pi * (4)^2 * (2000)^4. P2 = sigma * 4 * pi * (1)^2 * (4000)^4. Ratio P1/P2 = (16 * 2000^4) / (1 * 4000^4) = 16 / 16 = 1. The ratio is 1:1.

Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice laws of heat transfer heat and thermodynamics physics

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.