THERMAL CONDUCTION AND RADIATION FACULTY-RSP

SECTION-I
Single Correct Answer Type 8 Q. [3 M (–1)]
1. The space between two concentric sphere of radius R1 = 3m and R2 = 5m is filled with a material of

thermal conductivity k æç k = 400 J ö÷ . Inner and outer surfaces are maintained at 200 K and 500 K
è smK ø
respectively. find distance from the centre where the temperature is 350 K :-

R1

R2
R
(A) 4.5 m (B) 4m (C) 3.75 m (D) 4.33 m
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r
2. A thick spherical shell of inner and outer radii r and R respectively has thermal conductivity k = ,
xn
where r is a constant and x is distance from the center of the shell. The inner and outer walls are
maintained at temperature T1 and T2 (< T1). The value of number n (call it n0) for which the temperature
gradient remains constant throughout the thickness of the shell will be:-
(A)1 (B) 2 (C) 3 (D) 4
3. An object of mass 1kg and specific heat capacity 100 J/kg–°C at temperature 50° C is placed in
surrounding at temperature 20°C. A heater of power 100 W is required to keep the temperature steady
at 50°C. The power of heater is doubled at t = 0, the temperature of the object at t = 30 sec is approximately
(Assume Newton's law of cooling to be valid) :-
(A) 54°C (B) 58°C (C) 69°C (D) 80°C
4. A spherical black body of radius r at absolute temperature T is surrounded by a thin spherical and
concentric shell of radius R, black on both sides. The factor by which this radiation shield reduces the
rate of cooling of the body (consider space between spheres evacuated, with no thermal conduction
losses) is given by the following expression: aR2/(R2 + br2). a and b are numerical coefficient. The ratio

a
is
b
(A) 2 (B) 4 (C) 1 (D) 7
5. A 100 watt light bulb has a tungsten filament. (Emissivity e = 0.30) which required to operate at 2780
K. If the bulb is completely evacuated. Calculate the minimum surface area of the tungsten filament.
Assume that no radiant energy strikes the bulb surface and that steady state conditions prevail.
(A) 0.98 × 10–4 m2 (B) 1.92 × 10–4 m2 (C) 0.64 × 10–3 m2 (D) 1.40 × 10–5 m2
6. An Electric kettle is used to heat m = 1.8 kg of water. During the time t1 = 2 min, water temperature
increased from t1 = 85° C to t2 = 90° C. After turning off the kettle water temperature decreased by one
degree during the time t2 = 1 min. What is the approximate power P of the boiler? Specific heat of water
C = 4200 J/(kg-K).
(A) 341 W (B) 441 W (C) 541 W (D) 641 W
7. Two parallel black plates of area 1m are maintained at a temperature of 500k and 300k respectively.
2

The plates are separated by a distance of 1mm. When region between plates is evacuated, heat flows
dQ
from 1 plate to another plate at a certain rate . If the gap is filled with a material of thermal conductivity
dt
k, the rate of heat flow remains the same as before. What is value of k? Take : s = 5.67 × 10–8 W/m2k4
(A) 1.54 × 10–2 W/mk (B) 7.36 × 10–3 W/mk (C) 4.15 × 10–4W/mk (D) 6.26 × 10–2 W/mk
8. It is known that the temperature in the room is +20°C when the outdoor temperature is -20°C, and
+10°C when the outdoor temperature is –40°C. Then the temperature T of the radiator heating the room
is (Assuming that radiated by the heater is proportional to the temperature difference with the room).
(A) 40° C (B) 60° C (C) 30 °C (D) 20 °C
Multiple Correct Answer Type 6 Q. [4 M (–1)]
R
9. A copper rod and a steel rod of equal cross-sections and lengths (L) are joined side by side and connected
between two heat baths as shown in the figure. If heat flows through them from x = 0 to x = 2L at a
SP
steady rate and conductivities of the metals are Kcu & Ksteel (Kcu > Ksteel), then the heat current (i) and
temperature (T) varies with x as: (convection and radiation heat loss are negligible)
X=0 X=L X = 2L

Cu Steel

i (Heat current) T

(A) (B)

x=0 x = 2L x=L x = 2L

i (Heat current)
T

(C) (D)
x
L 2L x=0 x = 2L
10. The power radiated by two spherical black bodies consists of electromagnetic waves of different
wavelengths. The Power radiated by the body corresponding to wavelength l to l + dl is dP. dP/dl is
plotted against l. If the area under the graphs are equal,

dP (A)
(B)
dl

l
lA lB

(A) Temperature of A is more than that of B (B) Temperature of A is less than that of B
(C) The radius of A is less than that of B (D) The radius of A is more than that of B.
11. A highly thin conducting spherical shell of radius R0 is completely filled with water at 0°C. Outside
surrounding temperature is –T0°C. Latent heat of fusion of water is L0 and thermal conductivity of ice is
Kice. Assume heat is flowing symmetrically in radial direction. Choose the CORRECT option(s). Density
of water is r0. Neglect the expansion of water on freezing.

ice
R
Water at 0°C
Surrounding at
SP
–T0 °C
F

R0
Highly conducting
thin shell

r0 L0 R20
(A) Time in which complete water will freeze, is given by
6K ice T0

r0 L0 R20
(B) Time in which complete water will freeze, is given by
4K ice T0

R0 r0 L 0 R20
(C) Time in which thickness of ice will become , is given by
2 12K iceT0

4 pr0 L0 R03
(D) Total heat released by water in freezing, is given by
3
12. Thin metal disc of thickness t is hung out in air at a temperature T = 300.0 K. The upper surface of the
disk is illuminated by sunlight, which causes the disk to heat up: the temperature of its lower surface
Tb = 340.0 K, and the temperature of the upper Tt = 360.0 K. Consider that the air temperature near the
disk does not change, and the energy that the disk loses from a unit surface per unit time due to heat
transfer is proportional to the difference between the temperatures of its surface and air. Find out what
temperatures Tt and Tb would the upper and lower surfaces of the disk have, if its thickness were equal
to 2t.
(A) Tt = 366.67 K (B) Tb = 333.33 K (C) Tt = 350 K (D) Tb = 325 K
13. A conducting cylinder has curved surface covered with insulated layer. Flat surfaces are perfect absorbers.

3 2
Flat surface area is m . A point light source placed at some distance from left face. Temperature of
17
surrounding is 0 K. In steady state temperature of left face is 200 K and right face 100 K. Neglect heat

17
transfer by radiation between the flat surfaces. Then (Stefan's constant = ´10 -8 W/m2k4)
3

(A) Power emitted by source is 68 W.

(B) Power emitted by source is 18 W.
R

(C) Thermal conductivity of cylinder is 0.057 W/mK

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(D) Thermal conductivity of cylinder is 0.023 W/mK
14. A large sheet of area 1 m2 is kept 1 mm away from a thick sheet of thickness 4 mm and thermal
conductivity k and area 1m2 as shown. The left sheet is kept at a temperature of 327 °C and the left face
of thick sheet is found to be at 127 °C. The emissivity of the left sheet is 'e' where as both surfaces of the
thick sheet are blackened. The right face of thick sheet is found to be at 27°C. Surrounding is vacuum.

æ 17 -8 2 4ö
ç s = 3 ´ 10 W / m K ÷
è ø

(A) The power radiated by right surface of thick sheet is 459 W.

(B) The thermal conductivity of thick sheet is 9.18 × 10–3 W/mK.

81
(C) The emissivity e is .
1040
(D) If emissivity e is increased, temperature of left as well as right face of thick sheet increases.
Matching List Type (4 × 4) 1Q. [3 M (–1)]
15. Match the List- I with List- II.
List- I List- II

A B
E
(P) 200ºC F (1) 28ºC
20ºC
D

Conductivity of each rod = k

all rods are identical TC = ? ?

A 2k B k C
0ºC
50ºC
R
3k
(Q) (2) 66.67ºC
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D 100ºC

Conductivity of rods AB = 2K
BC = K
BD = 3K
all are of same length and area
TB = ? ?

1 kg ice + 2 kg H2O
(R) 0ºC 80ºC (3) 26.67ºC

Final temp after mixing them in isolation = ? ?

(S) Body cools through radiation (4) 110ºC

from 60ºC to 40ºC in 7 minute
Tsurrounding = 10ºC
What will be its temp after next 7 minute
Codes :-
P Q R S
(A) 4 2 3 1
(B) 1 2 3 4
(C) 3 2 4 1
(D) 1 4 2 3
 SECTION-II
Numerical Answer Type Question 6 Q. [3M(0)]
(upto second decimal place)
16. Consider a rod of length 1m. One of the ends of the rod is maintained at 100°C.The other end is at 0°C.
At the distance of 25 cm from the end at higher temperature, there is a heat source giving heat at a
constant rate of 80 W to the rod. The area of the rod is 100 cm2 and coefficient of thermal conductivity
is 50 W/mK. What is the temperature of the heat source? (in °C)
17. After the warm days, a sharp frost hit a lake and its surface got covered with ice. One day after the cold
snap; the ice thickness was d1 = 2 cm. Some ship builders want to take weights on the opposite shore of
the lake. But for security reasons ice thickness of at least d2 = 10 cm is needed. How many days after
moment of frost is it possible to transport the goods, if the temperature of surrounding does not change.
18. An electric heater is used in a room of total wall area 50 m2 to maintain a constant temperature of 15°C
inside when the outside temperature is –10°C. The walls have two different layers. The inner layer is of
cement of thickness 2 cm, while the outer layer is of brick of thickness 10 cm. Assume that there is no
loss of heat from the floor and the ceiling. Take the thermal conductivities of cement and brick to be 0.2
W/m°C and 0.5 W/m°C, respectively. If another identical heater is now switched on, along with the old
heater (having wattage found above) and the outside temperature has now dropped to –15°C. The
steady state temperature (in °C) inside the room is.
19. Mad scientist Knox has found a way to stop global warming. To do this, he wants to increase the radius
R
r of the Earth's orbit, which is assumed to be circular, by 1.0%. How much could the average temperature
T on the earth's surface decrease (in K), which is currently around 15 °C?
SP
20. It is known that the peak radiation from the sun has a maxima at 500 nm. The total energy emitted by the
sun is 4 times that emitted by another star whose radiation has a maxima at 400 nm. What is the ratio of
the radius of sun and the radius of the star? Assume that both of them radiate like a black body.
21. Two long coaxial cylindrical shells are both black bodies and very good thermal conductors. The radius
of the inner cylinder is 1 cm and the radius of the outer cylinder is 15 cm. There is a source of heat inside
the inner cylindrical shell which supplies heat at a constant rate of 1.7p W for every unit length of the
shell. If stefan’s constant is 17/3 ×10–8 W/m2K4, what is the steady state temperature of the inner shell (in
K)?
SECTION-III
Numerical Grid Type (Ranging from 0 to 9) 5 Q. [4 M (0)]
22. A cylinder of ice is made inside an insulated cup as shown. The bottom of cup is a plate of thermal
conductivity 3.35 W/mK. It's other side is at 100°C. Density of ice = 0.9 gm/cc, density of water = 1 gm/
1
cc. What is the downward speed v of the top surface (in mm/s). L = 3.35 × 105 J/kg. Fill in OMR
v
sheet.

20cm

ice
1m at
0°C

1mm

T=100°C
 242
23. Two containers A and B are connected by a conducting solid cylindrical rod of length cm and
7
radius 8.3 cm. Thermal conductivity of the rod is 693 watt/mK. The container A contains two mole of
oxygen gas and the container B contains four mole of helium gas. At time t = 0 temperature difference
of the containers is 50ºC, after what time (in seconds) temperature difference between them will be
25ºC. Transfer of heat takes place through the rod only. Neglect radiation loss. Take R = 8.3 J/mole-K
22
and p = .
7
A B
O2 He

24. A cylindrical rod of length 5m and cross–sectional area 1 m2 is fitted between a furnace and vacuum
chamber as shown in the figure. Only a small portion of the rod are inside the chambers and the rest is
thermally insulated from the surrounding. The end B of the rod is radiating like a black body. Under
steady state the wavelength l corresponding to the maximum energy radiated by end B is 2.89 mm. The
thermal conductivity of rod K = 60(10 + x) W/m–k where x is measured from A towards B.
The approximate temperature of furnace is found to be P times 200 Kelvin. Find P.
Wein’s constant = 2.89 x 10–3mK
R
Stephen’s constant = 6 x 10–8 W/m2–K4
æ3ö
(useful data ln çè 2 ÷ø = 0.4)
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A B

furnace vacuum chamber

at 27°C

25. A lizard of mass 4g is warming it self in the bright sunlight. It's surface area is 4.2 cm2, but its body casts
a shadow of area 1.4 cm2 on a piece of paper held perpendicular to sun rays. The intensity of sun rays at
earth is 1000 W/m2. Assume that specific heat capacity of lizard is same as that of water and its body
behaves like a black body, also neglect the radiation from the lizard's body. How long (in minutes) must
lizard lie in sun in order to raise it's temperature by 5°C. Specific heat capacity of water is 4200 J/kgºC.
n
If your answer is n fill value .
5
26. A spherical black body of radius R is arranged concentrically inside a hemispherical shell of a black
body of radius 2R as shown in the figure. The hemispherical body is maintained at a temperature T0.
Assuming that the sphere is perfectly conducting and the only mode of heat transfer between the sphere
and the rest of the universe is radiation. The temperature of the enclosure around the system is assumed
T0
to be zero Kelvin. The steady state temperature T of the sphere is . Find the value of a.
a1/4