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?

Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation.

If the surrounding temperature reduces by a small amount Δ T 0 < < T 0 , then to maintain the same body temperature the same (living) human being needs to radiate Δ W = 4 σ T 0 3 Δ T 0 more energy per unit time

If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths

The amount of energy radiated by the body in 1 second is close to 60 J o u l e s

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 rod of length $ℓ$ and cross section area $A$ has a variable thermal conductivity given by $k = α T$ , where $α$ is positive constant and $T$ is temperature in kelvin. Two ends of the rod are maintained at temperatures $T_{1}$ and $T_{2} (T_{1} > T_{2})$ . Heat current flowing through the rod will be

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Important Questions on Transmission of Heat

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 54

A refrigerator is thermally equivalent to a box of cork board 90 mm thick and 6 m² in inner surface area, the thermal conductivity runs 15% of the time while the door is closed. The inside wall of the door, when it is closed, is kept, on an average 22^oC below the temperature of the outside wall. The rate at which heat is taken from the interior wall while the motor is running is

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 55

Power radiated by a black body is

P_{0}

and the wavelength corresponding to maximum energy is around

λ_{0}

. On changing the temperature of the black body, it was observed that the power radiated becomes

\frac{256}{81} P_{0}

. The shift in wavelength corresponding to the maximum energy will be

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 56

The top of insulated cylindrical container is covered by a disc having emissivity $0.6$ and thickness $1 cm$ . The temperature is maintained by circulating oil as shown in figure. If temperature of upper surface of disc is $127 ° C$ and temperature of surrounding is $27 ° C$ , then the radiation lost to the surroundings will be (Take $σ = \frac{17}{3} \times 10^{- 8} W / m^{2} K^{4}$ )

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 57

Three rods AB, BC and BD of same length

l

and cross section A are arranged as shown. The end D is immersed in ice whose mass is 440 g and is at 0^oC. The end C is maintained at 100^oC. Heat is supplied at constant rate of 200 cal/s. Thermal conductivities of AB , BC and BD are K, 2K and K/2, respectively. Time (in seconds) after which whole ice will melt is (K = 100 cal/m-s-^oC, A = 10 cm²,

l

= 1 m)

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 58

A system receives heat continuously at the rate of 10 W. The temperature of the system becomes constant at 70^oC when the temperature of the surroundings is 30^oC. After the heater is switched off, the system cools from 50^oC to 49.9 ^oC in 1 min. The heat capacity of the system is

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 59

The earth receives on 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

7.0 \times 10^{8} m

. Treating sun as a block body, it follows from the above data that its surface temperature is

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 60

Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle $A B C$ , right angled at $B$ , as shown in the figure. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt{2} T$ , respectively, in the steady state. Assuming that only heat conduction takes place, temperature of point $C$ will be

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 61

Two hollow spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the times taken for complete melting of ice in the larger to the smaller one are in the ratio of

25 : 16

, then their corresponding thermal conductivities are in the ratio

A rod of length ℓ and cross section area A has a variable thermal conductivity given by k=αT, where α is positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperatures T1 and T2 T1>T2. Heat current flowing through the rod will be

Important Questions on Transmission of Heat

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