The earth receives at its surface radiation from the sun at the rate of 1400 W m - 2 . The distance of the centre of the sun from the surface of the earth is 1 . 5 × 10 11 m and the radius of the sun is 7 × 10 8 m . Treating the sun as a black body calculate the temperature of the sun. (Take σ = 5 . 67 × 10 - 8 W m - 2 K 4 )

Let R S be the radius of Sun and d be the distance of earth from centre of Sun. From Stefan's law, the power radiated by Sun is P = σ A T 4 = σ 4 π R S 2 T 4 where, σ is Stefan-Boltzmann constant, A is surface area and T is absolute temperature of sun. Intensity received by earth is = σ 4 π R S 2 T 4 4 π d 2 = σ R S d 2 × T 4 ⇒ 1400 = 5 . 67 × 10 - 8 7 × 10 8 1 . 5 × 10 11 2 × T 4 ⇒ T = 5800 K Hence, temperature of sun is 5800 K .

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?

The filament consumes less electrical power towards the end of the life of the bulb

The temperature distribution over the filament is uniform

The resistance over small sections of the filament decreases with time

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A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a cross section of the straight rod in a given time.

Important Questions on Heat Transfer

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 5

Three slabs of the same surface area but different conductivities $k_{1}, k_{2}, k_{3}$ and different thickness $t_{1}, t_{2}, t_{3}$ are placed in close contact. After steady state this combination behaves as a single slab. Find its effective thermal conductivity.

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 6

A hollow metallic sphere of radius

20 cm

surrounds a concentric metallic sphere of radius

5 cm

. The space between the two-sphere is filled with nonmetallic material. The inner and outer spheres are maintained at

50 ° C

and

10 ° C

, respectively, and it is found that

100 J

of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres.

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 7

A hollow tube has a length

l

, inner radius

R_{1}

and outer radius

R_{2}

. The material has thermal conductivity

K

. Find the heat flowing through the walls of the tube per second if the inside of the tube is maintained at a temperature

T_{1}

and the outside is maintained at

T_{2}

[assume

T_{2} > T_{1}

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 8

A metal rod of cross-sectional area

1.0 {cm}^{2}

is being heated at one end. At one time, the temperature gradient is

5.0 ° C {cm}^{- 1}

at cross-section

A

and is

2.5 ° C {cm}^{- 1}

at cross-section

B

. Calculate the rate at which the temperature is increasing in the part

A B

of the rod. The heat capacity of the part

A B = 0.40 J ° C^{- 1}

thermal conductivity of the material of the rod

=

200 W m^{- 1} ° C^{- 1}

. Neglect any loss of heat to the atmosphere.

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 9

When

q_{1}

joules of radiation is incident on a body it reflects and transmits a total of

q_{2}

joules. Find the emissivity of the body.

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 10

A blackbody of surface area

1 {cm}^{2}

is placed inside an enclosure. The enclosure has a constant temperature

27 ° C

and the blackbody is maintained at

327 ° C

by heating it electrically. What electric power is needed to maintain the temperature?

σ = 6.0 \times 10^{- 8} W m^{- 2} K^{- 4}

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 11

Estimate the temperature at which a body may appear blue or red. The values of

λ_{mean}

for these are

5000 Å

and

7500 Å

respectively. [ Given Wien’s constant

b = 0.3 cm K

]

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Alpha Question Bank for Engineering: Physics>Chapter 16 - Heat Transfer>Exercise - 1>Q 12

The earth receives at its surface radiation from the sun at the rate of

1400 W m^{- 2}

. The distance of the centre of the sun from the surface of the earth is

1.5 \times 10^{11} m

and the radius of the sun is

7 \times 10^{8} m

. Treating the sun as a black body calculate the temperature of the sun. (Take

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

)

Important Questions on Heat Transfer

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