A spherical object which behaves as a black body is raised to the temperature T 0 and placed in an environment whose temperature is, initially 0 ° C . While the object cools from T 0 to the temperature T c in an interval of time t = τ , the environment rises to the temperature t o ° C during the same time. The average rate of cooling of the object d T d t and the net heat loss Q of the object during the time interval 0 < t < τ 4 are respectively given by d T d t = α A and Q = β A while the same quantities during the interval 3 τ 4 < t ≤ τ are d T d t = α B and Q = β B . Assume Stefan's law is valid and read the following statement about this system. State which of the following statement(s) is/are true, by CORRECT choice from below :

The Newton's law of cooling will be valid whenever Stefan's law is valid

The rate of cooling decreases with time at first, reaches a minimum and then increases with time

MEDIUM

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A spherical object which behaves as a black body is raised to the temperature $T_{0}$ and placed in an environment whose temperature is, initially $0 ° C$ . While the object cools from $T_{0}$ to the temperature $T_{c}$ in an interval of time $t = τ$ , the environment rises to the temperature $t_{o} ° C$ during the same time. The average rate of cooling of the object $(\frac{d T}{d t})$ and the net heat loss $(Q)$ of the object during the time interval $0 < t < \frac{τ}{4}$ are respectively given by $(\frac{d T}{d t}) = α_{A}$ and $(Q) = β_{A}$ while the same quantities during the interval $\frac{3 τ}{4} < t \leq τ$ are $(\frac{d T}{d t}) = α_{B}$ and $(Q) = β_{B} .$ Assume Stefan's law is valid and read the following statement about this system. State which of the following statement(s) is/are true, by CORRECT choice from below :

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Important Questions on Thermal Properties of Matter

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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}}

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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)

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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)

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

If temperature of black body increases from

17 ° C

307 ° C,

then the rate of radiation increases by

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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?

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

If temperature of a black body increases from

300 K

900 K

, then the rate of energy radiation increases by

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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}

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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 $B ?$

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

The power radiated by a black body is P and it radiates maximum energy at wavelength,

λ_{0}

. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength

\frac{3}{4} λ_{0}

, the power radiated by it becomes nP. The value of n is

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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?

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

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

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Stefan’s Law

Assuming the sun to have a spherical outer surface of radius

r

, radiating like a black body at temperature

t ℃,

the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is

Where

σ

is the stefan's constant.

Important Questions on Thermal Properties of Matter

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