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A metallic sphere having radius $0.08 m$ and mass $m = 10 kg$ is heated to a temperature of $227 ° C$ and suspended inside a box whose walls are at a temperature of $27 ° C$ . The maximum rate at which its temperature will fall is (take $e = 1$ , Stefan's constant, $σ = 5 .8 \times 10^{- 8} W m^{2} K^{- 4}$ and specific heat of the metal $= 90 cal {kg}^{- 1} ° C^{- 1}, J = 4.2 J {cal}^{- 1}$ )

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Important Questions on Thermal Properties of Matter

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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>Thermal Properties of Matter>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

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Radiation

The "Kangri" is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the "Kangri" is spherical and of surface area

7 \times 10^{- 2} m^{2} .

It contains

300 g

of a mixture of coal, wood and leaves with calorific value of

30 kJ g^{- 1}

(and provides heat with

10 %

efficiency). The surface temperature of the 'Kangri' is

60 ° C

and the room temperature is

0 ° C .

Then, a reasonable estimate for the duration t (in hours) that the 'kangri' heat will last is (take the 'kangri' to be a black body):

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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)

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Radiation

A certain stellar body has radius

50 R_{s}

and temperature

2 T_{s}

and is at a distance of

2 \times 10^{10} AU

from the earth. Here,

AU

refers to the earth-sun distance and

R_{s}

and

T_{s}

refer to the sun's radius and temperature, respectively. Take, both star and sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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}

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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}

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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>Thermal Properties of Matter>Radiation

If temperature of black body increases from

17 ° C

307 ° C,

then the rate of radiation increases by

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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>Thermal Properties of Matter>Radiation

When the temperature of a body is increased from

27 ° C

127 ° C,

the radiation emitted by it increases by a factor of ________

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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?

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Radiation

Thermopile Bolometer is used to detect

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Radiation

Two spheres of same material and radii

5 m

and

2 m

are at temperature

200 K

and

250 K

respectively. The ratio of energies radiated by them per second is

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Radiation

If temperature of a black body increases from

300 K

900 K

, then the rate of energy radiation increases by

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>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}}

Important Questions on Thermal Properties of Matter

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