The two ends of a uniform rod of thermal conductivity k are maintained at different but constant temperatures. The temperature gradient at any point on the rod is d θ d l (equal to the difference in temperature per unit length). The heat flow per unit time per unit cross-section of the rod is I then which of the following statements is/are correct:

I will decrease as we move from higher to lower temperature

All the above options are incorrect

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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Seven identical rods of material of thermal conductivity $k$ are connected as shown in the given figure. All the rods are of identical length $l$ and cross-sectional area $A$ . If the one end $A$ is kept at $100 ° C$ and the other end $B$ is kept at $0 {}^{\circ}C$ , what would be the temperatures of the junctions $C, D$ and $E$ ( $θ_{C}$ $θ_{D}$ and $θ_{E}$ ) in the steady state?

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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 11

A circular ring (centre $O$ ) of radius $a$ , and of uniform cross-section is made up of three different metallic rods $A B, B C$ and $C A$ (joined together at the points $A, B$ and $C$ in pairs) of thermal conductivities $α_{1}, α_{2}$ and $α_{3}$ , respectively (see diagram). The junctions $A, B$ and $C$ are maintained at the temperatures $100 ° C, 50 ° C$ and $0 ° C$ , respectively. All the rods are of equal lengths and cross-sections. Under steady state conditions, assume that no heat is lost from the sides of the rods. Let $Q_{1}, Q_{2}$ and $Q_{3}$ be the rates of transmission of heat along the three rods $A B, B C$ and $C A$ . Then

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 12

Eleven identical rods are arranged as shown in figure. Each rod has length $l$ , cross-sectional area $A$ and thermal conductivity of material $K$ . Ends $A$ and $F$ are maintained at temperatures $T_{1}$ and $T_{2} (< T_{1})$ , respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer $(\frac{d Q}{d t})$ in each rod is

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 13

Two spheres

A

and

B

have same radius but the heat capacity of

A

is greater than that of

B

. The surfaces of both are painted black. They are heated to the same temperature and allowed to cool. Then:

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 14

The two ends of a uniform rod of thermal conductivity

k

are maintained at different but constant temperatures. The temperature gradient at any point on the rod is

\frac{d θ}{d l}

(equal to the difference in temperature per unit length). The heat flow per unit time per unit cross-section of the rod is

I

then which of the following statements is/are correct:

EASY

Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 15

Two ends of area

A

of a uniform rod of thermal conductivity

K

are maintained at different but constant temperatures. At any point on the rod, the temperature gradient is

\frac{d T}{d l}

. If

I

be the thermal current in the rod, then:

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 16

A metal cylinder of mass

0.5 kg

is heated electrically by a

12 W

heater in a room at

15 ° C

. The cylinder temperature rises uniformly to

20 ° C

in 5 min and finally becomes constant at

45 ° C

. Assuming that the rate of heat loss is proportional to the excess temperature over the surroundings:

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 17

Two spherical black bodies

A

and

B

, having radii

r_{A}

and

r_{B} = 2 r_{A}

emit radiation with peak intensities at wavelength

400 nm

and

800 nm

respectively. If their temperature are

T_{A}

and

T_{B}

respectively in Kelvin scale, their emissive powers are

E_{A}

and

E_{B}

then:

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 2 - Transmission of Heat>Exercises>Q 1

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:

Important Questions on Transmission of Heat

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