From the figure, what’s the relation between T 1 , T 2 , and T 3 ?

We already know, as the temperature of the body is higher, the intensity of the black body radiations would be higher. Thus, from the graph, the radiations with temperature T 3 has the highest intensity followed by the one with temperature T 2 and then T 1 . Thus, T 3 > T 2 > T 1 . <img alt="This graph shows the variation of blackbody Radiation intensity with wavelengths expressed in micrometers. Five curves that correspond to 2000 K, 3000 K, 4000 K, and 5000 K are drawn. The maximum of the radiation intensity shifts to the short-wavelength side with increase in temperature. It is in in the far-infrared for 2000 K, near infrared for 3000 K, red part of the visible spectrum for 4000 K, and green part of the visible spectrum for 5000 K." src="https://sss.embibe.com/content-grail/preprod/4ec4de38-537d-4a6d-97ca-52a59fb54b89.jpg" />

From the figure, what’s the relation between T 1 , T 2 , and T 3 ?

We already know, as the temperature of the body is higher, the intensity of the black body radiations would be higher. Thus, from the graph, the radiations with temperature T 3 has the highest intensity followed by the one with temperature T 2 and then T 1 . Thus, T 3 > T 2 > T 1 . <img alt="This graph shows the variation of blackbody Radiation intensity with wavelengths expressed in micrometers. Five curves that correspond to 2000 K, 3000 K, 4000 K, and 5000 K are drawn. The maximum of the radiation intensity shifts to the short-wavelength side with increase in temperature. It is in in the far-infrared for 2000 K, near infrared for 3000 K, red part of the visible spectrum for 4000 K, and green part of the visible spectrum for 5000 K." src="https://sss.embibe.com/content-grail/preprod/4ec4de38-537d-4a6d-97ca-52a59fb54b89.jpg" />

EASY

Earn 100

From the figure, what’s the relation between T₁, T₂, and T₃?

Important Questions on Kinetic Theory of Gases and Radiation

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A human body has a surface area of approximately

1 m^{2}

. The normal body temperature is

10 K

above the surrounding room temperature

T_{0}

. Take the room temperature to be

T_{0} = 300 K

. For

T_{0} = 300 K

, the value of

σ T^{4} = 460 W m^{- 2}

(where

σ

is the Stefan-Boltzmann constant). Which of the following options is/are correct?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A spherical black body with a radius of

12 cm

radiates

450 W

power at

500 K

. If the radius were halved and the temperature doubled, the power radiated in watt would be

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

Parallel rays of light of intensity

I = 912 W m^{- 2}

are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant

σ = 5.7 \times 10^{-8} W m^{- 2} K^{- 4}

and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

If temperature of a black body increases from

300 K

900 K

, then the rate of energy radiation increases by

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

The rate of radiation of a black body at

0 ° C

E

joule per sec. Then, the rate of radiation of this black body at

273 ° C

will be

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

The filament of a light bulb has surface area $64 {mm}^{2} .$ The filament can be considered as a black body at temperature $2500 K$ emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of $100 m$ . Assume the pupil of the eyes of the observer to be circular with radius $3 mm$ . Then:

(Take Stefan-Boltzmann constant $= 5.67 \times 10^{- 8} W m^{- 2} K^{- 4},$ Wiens' displacement constant $= 2 .90 \times 10^{- 3} m K$ , Planck's constant $= 6 .60 \times 10^{- 34} J s$ , speed of light in vacuum $= 3 .00 \times 10^{8} m s^{- 1}$ )

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with a vacuum inside. The walls of the cavity are maintained at temperature $T_{0}$ . The initial temperature of the sphere is $3 T_{0}$ . If the specific heat of the material of the sphere varies as $α T^{3}$ per unit mass with the temperature $T$ of the sphere, where $α$ is a constant, then the time taken for the sphere to cool down to temperature $2 T_{0}$ will be

( $σ$ is Stefan Boltzmann constant)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A mass

M

is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes

S . H . M .

of period

T

. If the mass is increased by

m

, the time period becomes

\frac{5 T}{3} .

What is the ratio

(\frac{M}{m})

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A small object is placed at the centre of a large evacuated hollow spherical container. Assume the container is maintained at

0 K

. At time

t = 0

, the temperature of the object is

200 K

. The temperature of the object becomes

100 K

t = t_{1}

and

50 K

t = t_{2}

. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio

(\frac{t_{2}}{t_{1}})

_________ .

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A black body is at a temperature of

5760 K.

The energy of radiation emitted by the body at wavelength

250 nm

U_{1}

, at wavelength

500 nm

U_{2}

and that at

1000 nm

U_{3}

. Wien's constant,

b = 2.88 \times 10^{6} nm K.

Which of the following is correct?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

Earth receives Sun's radiation at the rate of

P W m^{- 2}

. Mean distance between the Sun and the Earth is

r m

. Radius of the Sun is

R m

. If Stefan's constant is

σ

(in

SI

units), surface temperature of the Sun, in kelvin, is

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

Two spheres

S_{1}

and

S_{2}

have same radii but temperatures

T_{1}

and

T_{2}

respectively. Their emissive power is same and emissivity is in the ratio

1 : 4

Then the ratio of

T_{1}

T_{2}

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

The maximum wavelength of radiation emitted by a star is

289.8 nm

. Then intensity of radiation for the star is (Given : Stefan’s constant =

5.67 \times 10^{- 8} W m^{- 2} K^{- 4}

, Wien’s constant,

b = 2898 μm K)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

If the emission rate of a blackbody at

0 ° C

R

, then the rate of emission at

273 ° C

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

If temperature of black body increases from

17 ° C

307 ° C,

then the rate of radiation increases by

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

Two black bodies $A$ and $B$ have equal surface areas and are maintained at temperatures $27 ° C$ and $177 ° C$ respectively. What will be the ratio of the thermal energy radiated per second by $A$ to that by $B ?$

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

Two spherical black bodies have radii

r_{1}

and

r_{2}

. Their surface temperatures are

T_{1}

and

T_{2}

. If they radiate same power then

\frac{r_{2}}{r_{1}}

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A black body at a temperature

227 ° C

radiates heat at the rate of

5 cal {cm}^{- 2} s^{- 1} .

At a temperature of

727 ° C,

the rate of heat radiated per unit area is approximately

cal {cm}^{- 2} s^{- 1}

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Stefan's Law of Radiation

A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature are allowed to cool down under similar conditions. Then the

From the figure, what’s the relation between T1, T2, and T3?

Important Questions on Kinetic Theory of Gases and Radiation

Learn and Prepare for any exam you want !

From the figure, what’s the relation between T₁, T₂, and T₃?