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What is energy density write its formula?

Important Questions on Kinetic Theory of Gases and Radiation

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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?

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

In the case of black body for energy distribution, energy radiated by a blackbody which is given by, Planck's formula reduces to Rayleigh Jean's formula for

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

If the surface is a perfect reflector, the change in momentum of the wave after falling on the surface is

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

A body cools from a temperature

3 T

2 T

10

minutes. The room temperature is

T

. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next

10

minutes will be

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

Heat energy is incident on the surface of a material at the rate of

1000 J \min^{- 1}

. If the coefficient of absorption is

0.8

and the coefficient of reflection is

0.1

, then the amount of heat energy transmitted through the material in

5 minutes

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

On observing light from three different stars

P

Q

and

R

, it was found that intensity of violet colour is maximum in the spectrum of

P

, the intensity of green colour is maximum in the spectrum of

R

and the intensity of red colour is maximum in the spectrum of

Q

. If

T_{p}, T_{Q}

and

T_{R}

are the respective absolute temperatures of

P

Q

and

R

, then it can be concluded from the above observations that :

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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}

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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?

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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 $= 3 .00 \times 10^{8} m s^{- 1}$ )

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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}}

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

In Raman effect, the spectral line with lower frequency than the incident frequency is

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

If a piece of metal is heated to temperature

θ

and then allowed to cool in a room which is at temperature

θ_{0}

, the graph between the temperature

T

of the metal and time

t

will be closest to :

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

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)

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

Certain quantity of water cools from

70^{o} C

60^{o} C

in the first

5

minutes and to

54^{o} C

in the next

5

minutes. The temperature of the surroundings is:

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

Two identical beakers

A

and

B

contain equal volumes of two different liquids at

60 ° C

each and left to cool down. Liquid in

A

has density of

8 \times 10^{2} k g m^{- 3}

and specific heat of

2000 J k g^{- 1} K^{- 1}

while the liquid in

B

has density

10^{3} k g m^{- 3}

and specific heat of

4000 J k g^{- 1} K^{- 1}

. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

A container with $1 kg$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 W m^{- 2}$ and it is absorbed by the water over an effective area of $0.05 m^{2} .$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ}C$ ) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $= 0.001 s^{- 1},$ Heat capacity of water $= 4200 J {kg}^{- 1} K^{- 1}$ )

(Approximate the answer to two decimal place)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

For any material, if

R, T

and

A

represent the reflection coefficient, transparent coefficient and absorption coefficient respectively, then for a blackbody which one of the following is true

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Interaction of Thermal Radiation and Matter

What is the radiation pressure on earth's surface?

What is energy density write its formula?

Important Questions on Kinetic Theory of Gases and Radiation

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