Three rods of equal length L × 10 - 2 m and equal area of cross-section S × 10 - 4 m 2 are joined in series. The thermal conductivities of the materials are K × 420 , 2 K × 420 and 1 . 5 K × 420 S.I. units. If the open ends of the first and the last rods are at 200 ° C and 18 ° C . Calculate the temperature at the two junctions and the rate of flow of heat through the system neglecting radiation losses.

Heat rate, Q = K A ∆ T l For first rod, Q = ( K × 420 ) × A × ( 200 - T 1 ) l For second rod, Q = ( 2 K × 420 ) × A × ( T 1 - T 2 ) l For third rod, Q = ( 1 . 5 K × 420 ) × A × ( T 2 - 18 ) l Since heat released by the first rod is equal to the heat gained by second rod, we get ⇒ Q = ( K × 420 ) × A × ( 200 - T 1 ) l = ( 2 K × 420 ) × A × ( T 1 - T 2 ) l ⇒ ( 200 - T 1 ) = 2 T 1 - 2 T 2 ⇒ 3 T 1 = 200 + 2 T 2 Since heat released by the second rod is equal to the heat gained by third rod, we get ⇒ Q = ( 2 K × 420 ) × A × ( T 1 - T 2 ) l = ( 1 . 5 K × 420 ) × A × ( T 2 - 18 ) l ⇒ 2 ( T 1 - T 2 ) = 1 . 5 ( T 2 - 18 ) ⇒ 2 T 1 = 3 . 5 T 2 - 27 dividing both equations, we get, 3 2 = 200 + 2 T 2 3 . 5 T 2 - 27 ⇒ 10 . 5 T 2 - 81 = 400 + 4 T 2 ⇒ 6 . 5 T 2 = 481 ⇒ T 2 = 74 ° C Substituting this in one equation, we get, 3 T 1 = 200 + 2 ( 74 ) 3 T 1 = 200 + 148 ⇒ T 1 = 116 ° C Heat rate, Q = K A ∆ T l ⇒ Q = ( K × 420 ) × ( S × 10 - 4 ) × ( 200 - 116 ) L × 10 - 2 = ( K × 420 ) × ( S × 10 - 2 ) × 84 L = 352 . 80 K S L

EASY

11th West Bengal Board

IMPORTANT

Earn 100

The thickness of each metal in a composite bar is $0.01 m$ and the temperatures of the two external surfaces are $100 ° C$ and $30 ° C$ . If the conductivities of the metals by $84$ S.I unit and $126$ SI unit respectively. Find the temperature on the interface.

Important Questions on Heat Transfer

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11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 19

What is the temperature of the steel-copper junction in the seady state of the system shown in Fig

19.38 a

. Length of the steel rod

= 0.150 m,

length of the copper rod

= 0.10 m

temperature of the furnace

= 300 ° C,

temperature of the other end

= 0 ° C

. The area of cross-section of the steel rod is twice that of the copper rod. Thermal conductivity of steel

= 50.2 {Js}^{- 1} m^{- 1 \circ} C^{- 1}

thermal conductivity of copper

= 385 {Js}^{- 1} m^{- 1} K^{- 1}

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 20

Two slabs A and B of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A a n d B a r e k_{1} a n d k_{2} r e s p e c t i v e l y .$ A steady temperature difference of $12 ° C$ is maintained across the composite slab. If $k_{1} = \frac{K_{2}}{2}$ the temperature difference across slab $A$ is:

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 21

Three rods of equal length

L \times 10^{- 2} m

and equal area of cross-section

S \times 10^{- 4} m^{2}

are joined in series. The thermal conductivities of the materials are

K \times 420, 2 K \times 420

and

1.5 K \times 420

S.I. units. If the open ends of the first and the last rods are at

200 ° C

and

18 ° C

. Calculate the temperature at the two junctions and the rate of flow of heat through the system neglecting radiation losses.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 1

A uniform glass U-tube is partially filled with a liquid. Horizontal length of the tube is $1 m$ . Tube is accelerating horizontally with constant acceleration of $6 m s^{- 2}$ . The difference in the heights of the liquid in the two arms of U-tube is-

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11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 2

A room is

7 m

5 m

3 m

and the walls are of brick

20 cm

thick and have windows of glass

0.05 cm

thick and of total area

5 m^{2}

. The temperature of the room is

20 ° C

higher than that outside. Calculate approximately the quantity of heat that is passing out per minute through the wall and the windows of the room. The thermal conductivity of brick and glass may be taken as

12 \times 10^{- 4}

and

17 \times 10^{- 4}

c.g.s. units respectively.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 3

A room is maintained at

20 ° C

by a heater of resistance of

20 Ω

connected to

200

volt mains. The temperature is uniform throughout the room and the heat is transmitted through a glass window of area

1 m^{2}

and thickness

0.2 cm

. Calculate the temperature outside. Thermal conductivity of glass is

0.67 W m^{- 1} K^{- 1}

and mechanical equivalent of heat is

4.2

joules / cal.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 4

The temperature gradient in the earth's crust is

32 ° C

per

km

, and the mean conductivity of rocks is

0.08 c . g . s .

units. Taking the radius of the earth as

6000 km

, calculate the daily loss of heat by the earth by conduction.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 18 - Heat Transfer>EXERCISE>Q 5

A rod

C D

is joined at the middle of an identical rod

A B

. The length, the area of crosssection and thermal conductivity of each rod are

l, α

and

K

respectively [in fig]. The ends

A, B

and

D

are maintained at temperature

T_{1} T_{2}

and

T_{3} (T_{1} > T_{2} > T_{3})

respectively. Find the temperature at

C

Question Image

The thickness of each metal in a composite bar is 0.01 m and the temperatures of the two external surfaces are100°C and 30°C . If the conductivities of the metals by 84 S.I unit and 126 SI unit respectively. Find the temperature on the interface.

Important Questions on Heat Transfer

Learn and Prepare for any exam you want !

The thickness of each metal in a composite bar is $0.01 m$ and the temperatures of the two external surfaces are $100 ° C$ and $30 ° C$ . If the conductivities of the metals by $84$ S.I unit and $126$ SI unit respectively. Find the temperature on the interface.