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Thermal Expansion â?– Illustrative Examples 1) If the temperature in a room is 20oC, what is its temperature in degree Fahrenheit? Data :
(Ans. :
)
2) The normal boiling point of liquid oxygen is -183oC. What is this temperature in Kelvin scale. Data :
(Ans. :
)
3) At what temperature do the Kelvin and Fahrenheit scale coincide? (Ans. :
)
4) When the pressure of 1 litre of gas at 270C is doubled, its temperature rises to 1140C. Calculate the final volume of a gas. Data :
(Ans.
)
5) The length of a metal rod increases by 1.2cm when its temperature is increased to 390oC from 30oC. Determine the original length of the road. Data :
(Ans. :
)
6) A thin iron plate has a length of 25 cm and breadth of 15 cm at 20oC. Find its area when it is heated to 160oC. (Given :
for iron
)
Data :
(Ans. :
)
7) A metal ball of 0.2m radius is heated from 273oC to 348oC. Calculate the increase in surface area of the ball. (Coefficient of superficial expansion = 0.000036 K)
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Data : (Ans. :
)
8) How much heat is required to raise temperature of 500 g of kerosene from 10oC to 40oC? Given : The specific heat of kerosene is 0.51 kcal/kg oC. Data : Mass of kerosene = 500 g = 0.5 kg Rise in temperature,
= 40-10 = 30oC
Specific heat of kerosene = 0.51 k cal/kg oC.
(Ans. :
)
9) The volume of a metal sphere increases by 1.4% when it is heated from 30oC to 240oC. Determine coefficient of superficial expansion and coefficient of cubical expansion of metal. Data :
(Ans. : 10)
)
Calculate the temperature difference between two sides of an iron plate 2cm thick, when heat is transmitted through the plate at the rate of 600 kcal per minute per square meter at steady state. Thermal conductivity of iron is 0.02 kcal/msK. Data :
(Ans. : 11)
)
Calculate the rate of loss of heat through a glass window of area 1000 cm2 and thickness of 4mm, when temperature inside is 37oC and outside is -5oC. Coefficient of thermal conductivity of glass 0.022
.
Data : A = 1000cm2 K = 0.022 cal/s cmoC Thickness =
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Temperature difference 12)
The metal sphere cools at the rate of
(Ans. :
)
When its temperature is 70oC. At
what rate will it cool when its temperature is 40oC? The temperature of the surrounding is 30oC.
Data :
(Ans.
)
� Theory Question 1) What do you understand by the term temperature and heat'? 2) What are different scales of thermometer? What is the relation between them? 3) What is the importance of gas thermometer? 4) Write a short note on absolute scale of temperature. 5) What is triple point of water? 6) Derive ideal gas equation, PV = nRT. 7) Define - coefficient of linear expansion, coefficient of superficial expansion and coefficient of cubical expansion of solids. State their units. 8) Define principal and molar specific heat of a gas at i) constant volume and ii) constant pressure. 9) Why do we generally consider two specific hears of a gas? 10) What is calorimetry? 11) Explain the term – i) Latent heat of fusion ii) Latent heat of vaporisation. 12) Explain the process of conduction of heat through metal rod. Why are metals good conductors of heat as well as electricity? 13) Explain the term steady state. 14) Give any two applications of thermal conductivity in every day life. 15) What is the significance of thermal conductivity? 16) Describe process of transfer of heat try convection. Give any two applications of convection. 17) Describe the process of heat transfer by radiation. 18) Give reasons i) Stainless steel cooking pan is fitted with copper bottom. ii) Two layers of cloth used to cover the retain body heat better than a single layer of cloth having double the thickness.
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iii) Beakers crack when not water is poured in it. iv) We can hold our fingers beside the candle without harm but not above the flame. v) In summer one should wear white clothes and in winter one should wear black clothes. 19) State Newton’s law of cooling. Explain how it can be experimentlly verified. 20) What is thermal energy or internal energy of a body? OR Explain heat and temperature on the basis of thermal energy. 21) Define the following terms. i. Heat ii. Temperature 22) State the S.I. unit of the following. i. Heat energy ii. Temperature 23) Explain with example how heat energy is transferred between system and its surrounding. 24) What is thermometer? Explain with examples, the thermometric property used in a thermometer. 25) Define the following terms. i. Ice point ii. Boiling point 26) Draw a neat and well labelled diagram to show comparison of Kelvin, Celsius and Fahrenheit temperature scales. 27) Answer the following: i. The triple-point of water** is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)? ii. The absolute temperature (Kelvin scale) T is related to temperature tc on the Celsius scale by tc = T - 273.15. Why do we have 273.15 in this relation and not 273.16? 28) State Boyle’s law and give its formula. 29) State Charles’ law and give its formula. 30) Give the significance of absolute zero. 31) What is thermal expansion? 32) Define the following terms. i. Coefficient of thermal expansion.
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ii. Isotropic solids. iii. Linear expansion of solids. 33) Why do solids possess definite shape and size? 34) Why do solids expand on heating? 35) Derive an expression for the coefficient of linear expansion in solid. 36) Define superficial expansion in solid. 37) What is cubical expansion of a solid? Derive an expression for the coefficient of cubical expansion.
38) State the relation between
and
and write their meaning.
39) Write a short note on anamolous behaviour of water. 40) Explain advantage of anomalous behaviour of water in environment. 41) Derive an expression for the compressive force exerted by the supports on the rod, if one tries to prevent thermal expansion of a rod by fixing it to rigid support. 42) Two bodies at different temperatures are brought in thermal contact, do not necessarily settle to the mean temperature. Explain. 43) Define specific heat or specific heat capacity of a substance and obtain an expression for it. Give SI and CGS unit of specific heat. 44) Explain why specific heat capacity of a gas at constant pressure is greater than that at constant volume. 45) What do you mean by an isolated system? 46) Write a short note on calorimeter. 47) What do you mean by change of state? 48) Define latent heat of a substance. State its SI unit and CGS unit. 49) Define: i. Conduction Radiation.
ii. Convection
iii. Radiation
50) State conditions for conduction of heat. Explain process of conduction in solid. 51) What are good conductors and insulators of heat? OR Define good conductors and bad conductors. 52) Explain why metals are good conductors of heat and electricity. 53) State the characteristics of transfer of heat by conduction. 54) What is temperature gradient? State its units and dimensions. 55) What is coefficient of thermal conductivity of material? Write down its units and dimensions. 56) Why are cooking utensils provided with handle made up of wood or plastic fibre? 57) What are convection currents?
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58) State the characteristics of mode of transfer by convection. 59) Describe formation of sea breeze and land breeze using convection process. 60) State the characteristics of:
a. Sea breeze,
b. Land breeze
61) Explain why: i. a brass tumbler feels much colder than a wooden tray on a chilly day. ii. heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water. 62) State the characteristics of mode of transfer by radiation. 63) Is thermal conductivity of metals and non metals same?
❖ Textbook Problems 1) The length of metal rod is 150 cm at 250C. Find its length when it is heated to 150oC (Ans : 150. 4 cm) 2) A metal rod, 1.8m long increases in length by 1.4 mm when heated from 0oC to 50oC. Find the coefficient of linear expansion of metal.
(Ans :
)
3) The difference between the lengths of a steel rod and a brass rod is 0.6 m at all temperatures. What are their lengths at 0oC if
for brass =
steel
and
for
(Ans : 1.2 m, 1.8 m)
4) The surface area of the metal plate is 2.4 × 10-2 m2 at 20oC. When the plate is heated to 185oC, its area increases by 0.8 cm2. Find the coefficient areal expansion of metal. (Ans :
)
5) Calculate the difference in the temperature between the water at the top and bottom of a water fall 200m high. Specific heat of water is 4200J kg
(Ans : 0.467oC)
6) A certain mass of a gas at 20oC is heated until both its pressure and volume are doubled. Calculate its final temperature.
(Ans : 1172 K or 899oC)
❖ Practice Problems ➢ Type-I : Problems based on measurement of temperature 1) If the temperature in the room is 29 °C, what is its temperature in degree Fahrenheit?
(Ans : 84.2 °F.)
2) At what temperature do the Kelvin and Fahrenheit scales coincide? (Ans : 574.6 °F.)
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3) The triple points of neon and carbon dioxide are 24.57 K and 216.55 K, respectively. Express these temperatures on the Celsius and Fahrenheit scales. (Ans : -69.88 °F) 4) Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?
(And :
)
5) Alcohol boils at 78 °C. What is its temperature in Fahrenheit scale? (Ans : 172.4 °F) 6) The normal temperature of a healthy person is found to be 98.4 °F. What would be the corresponding reading on kelvin scale?
(Ans : 310.04 k)
7) On an oven, temperature is marked as 180 °F. What is the corresponding temperature on Celsius scale?
(Ans : 82.22 °C)
➢ Type-II : Problems based on ideal gas equation 8) When the pressure of 0.75 litre of a gas at 27 °C is doubled, its temperature rises to 111°C. Calculate the final volume of a gas.
(Ans : 480 cm3.)
9) One mole of a gas at pressure P1 and temperature 27 °C is heated till both pressure and volume are tripled. What is the temperature of the gas?
(Ans : 2700 K)
➢ Type-III : Problems based on thermal expansion 10) The length of a rail on a railway line is 25 m at 10 °C. During summer, maximum temperature attained in the region is 50 °C. Find the minimum gap between the rails, [
]
(Ans : 1.2 cm.)
11) A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper
(Ans :
)
12) The surface area of an iron plate is 80 cm2 at 20 °C. Find its surface area at 120 °C. (Ans : 80.2 cm2.) 13) A liquid occupies a volume of 2 × 10-4 m3 at 0 °C. Calculate the increase in its volume if it is heated to 80 °C. [The coefficient of cubical expansion of the liquid is 4 × 10-4 K-1]
(Ans :
)
14) On heating a glass block of 10,000 cm3 from 25 °C to 40 °C, its volume increases by 4 cm3. Calculate coefficient of linear expansion of glass.
(Ans :
)
15) A metal bar measures 60 cm at 10 °C. What would be its length at 110 °C? (Ans : 60.09 cm)
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16) A rod is found to be 0.04 cm longer at 30 °C than it is at 10 °C. Calculate its length at 0 °C.
(Ans : 100 cm)
17) Calculate the change in length of copper wire of length 50 cm when its temperature is raised by 70 °C. Coefficient of linear expansion for (Ans :
)
18) A thin copper disc has a hole of diameter 2 cm in the centre. Find the diameter of the hole when the temperature is increased by 15 °C. (Ans : d2 = 2.0005 cm) 19) Railway lines are laid with gaps to allow for expansion. The gap between two lines is 0.5 cm at 10 °C and the length of a line is 12 m. At what temperature will lines just touch?
(Ans : 47.8 °C)
20) When temperature of metal sphere of radius 5 cm is raised by 100 °C, its radius increases by 0.1 cm. Calculate
for metal.
21) The surface area of the metal plate is
(Ans :
)
at 25 °C when the plate is heated
to 200 °C, its area increases by 1.1 cm2. Find the coefficient of areal expansion of metal.
(Ans :
)
22) A sheet of brass is 40 cm long and 8 cm broad at 0 °C. If the area at 100 °C is 320.1 cm2, calculate the coefficient of linear expansion of brass.
(Ans :
)
23) Two rods A and B differ in length by 0.5 m at all temperatures. If and
find the lengths of the two rods at 0 °C.
(Ans : 0.5 m. 1 m)
24) Two metal rods A and B of different materials differ in length by 5 cm at all temperatures. What are their original lengths at 0 °C if the coefficient of linear expansion of A and B are
and
respectively? (Ans : A = 15 cm, B = 10 cm)
25) A rod P and a rod Q are of equal lengths at 0 °C. If at 100 °C, they differ in length by 1 mm, find their original lengths at 0 °C [
and
] (Ans : 250 cm)
➢ Type-IV : Problems based on specific heat capacity F.Y.J.C.
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26) How much heat is required to raise temperature of 750 g of copper pot from 20 °C to 50 °C? [The specific heat of copper is 0.094 kcal/kg °C]
(Ans : 2.115 kcal.)
27) An iron rod of 200 g is at temperature 2.8 °C. How much amount of heat will be required to raise the temperature to 88 °C? [Specific heat of iron is 0.11 cal g-1 k-1.] (Ans : 1320 cal) 28) A brass rod has an area of cross-section of 5 cm2 and has a length 50 cm. One end of the metal rod is maintained at 127 °C. The other end is at a lower temperature. If the quantity of heat flowing through the rod is 0.06 kcal/min, Find the temperature of the other end and temperature gradient along the rod. [Kbrass= 109.2 J/msK] (Ans : 88.5 °C, 77 °C/m)
➢ Type-V : Problems based on heat capacity 29) Heat is conducted through a copper plate at the rate of 460 cal/s-cm2. Calculate the temperature gradient when the steady state is reached. [Kcopper = 92 cal/m-s °C] (Ans : 5 °C/m) 30) Two parallel slabs of metals A and B of thickness 5 cm and 3 cm respectively are joined together. The outer face of the metal A is maintained at 100 °C and that of metal B is maintained at 40 °C. If the thermal conductivities of metal A and B are 0.045 kcal/m-s K and 0.015 kcal/m-s K respectively, find the temperature of the interface of two plates.
(Ans : 78.57 °C.)
31) A glass window has a length of 1 m, breadth 0.5 m and thickness 5 mm. The temperatures on two sides of the windows are 18 °C and -2 °C. If the thermal conductivity of the glass is 2 × 10-4 kcal/m-s K, calculate the heat conducted through the glass window per minute.
(Ans: 24kcal/min)
32) The temperature at the ends of a uniform rod of length 100 cm are respectively 95 °C and 5 °C. What will be the temperature at a point at a distance 30 cm from the hotter end?
(Ans : 68 °C)
33) A rectangular brass plate of sides 15 cm and 8cm with thickness 0.8 cm has its opposite faces maintained at 373 K and 343 K respectively. How much heat will flow through the plate per second? [K for brass = 109.2 W/mk.]
(Ans : 4914 J)
34) A wooden ice box contains ice at 0 °C. The inner dimensions of the box are and the wood is 4 cm thick. Find the rate at which ice would
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melt if the surrounding temperature is 32 °C. [K for wood = 0.168 S.I. units. Latent heat of fusion of ice = 336 J/g.]
(Ans : 0.832 kg/s)
35) A bar 0.2 m long and of cross-sectional area
is ideally bagged. One end
is maintained at 373 K and the other end is maintained at 273 K by surrounding it with melting ice. Calculate the rate at which ice melts owing to the flow of heat along the bar. [Thermal conductivity of material of bar = 400 W/mk, Latent heat of fusion of ice
]
(Ans :
)
➢ Type-VI : Problems based on Newton’s law of cooling 36) A body cools at the rate of 0.5 °C/s when it is at 50 °C above the surrounding temperature. What is its rate of cooling when it is at 30 °C above the surrounding temperature?
(Ans : 0.3 °C/s.)
37) A metal sphere cools at the rate of 3 °C/min when its temperature is 50 °C. Find its rate of cooling at 40 °C, if temperature of surrounding is 25 °C. (Ans : 1.8 °C/min) 38) A copper sphere cools from 80 °C to 70 °C in 5 minutes and to 48 °C in next 15 minutes. Find the surrounding temperature.
(Ans :
)
❖ Multiple Choice Question 1) The dimensional formula of coefficient of thermal conductivity is (A) [M1L1T-3K-1]
(B)[M1L2T-2K-1]
(C) [M1L1T-3K-4]
(D) [M1L0T-2K-1]
2) The most desirable combination for the material of a cooking pot is (A) high specific heat and high conductivity. (B) low specific heat and high conductivity. (C) high specific heat and low conductivity. (D) low specific heat and low conductivity.
3) While measuring thermal conductivity of a liquid, we keep the upper part hot and lower part cold, so that (A) radiation may start.
(C) convection may start.
(B) radiation may stop.
(D) convection may be stopped.
4) The superficial expansivity is 1 / x times the cubic expansivity. The value of x is (A) 2/3
(B) 3/2
(C) 2
(D) 3
5) Two rods of same material are equal in length, but one has cross-sectional area double the other. If they are heated through the same temperature then
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(A) thick rod expands more.
(C) both rods will expand equally.
(B) thin rod expands more.
(D) none of these.
6) A disc has an area of 0.32 m2 at 20 °C, what will be its area at 100 °C?
(A) 0.12 m2
(B) 0.32 m2
(C) 0.51m2
(D) 0.71m2
7) The volume of a metal block changes by 0.18% when it is heated through 20 °C. Its coefficient at cubical expansion will be (A)
(B)
(C)
(D)
8) The quantity of heat which crosses unit area of a metal plate during conduction depends on (A) the density of the metal. (B) the temperature gradient perpendicular to the area. (C) the temperature to which the metal is heated. (D) the area of the metal plate. 9) The coefficient of linear expansion of iron is
per K. An iron is 10 m long at
27 °C. Length of the rod will be decreased by 1.1 mm when the temperature of the rod changes to (A) 0°C 10)
(C) 17 °C
(D) 20 °C
An iron ball is heated. The percentage increase will be the largest in _______. (A) Diameter
11)
(B)10 °C (B) surface area
(C) volume
(D) density
One end of copper rod is in contact with water at 100 °C and the other end in contact with ice at 0 °C. The length of the rod is 100 cm. At a point which is at a distance of 35 cm from the cold end, temperature is (assuming steady state heat flow) (A) 35 °C
12)
(B) 65 °C
(C) 56 °C
(D) 53 °C
Iron sheet 50 cm × 20 cm is heated through 100 °C. If
the change
in area is (A) 2.4 cm2 13)
(B) 3.4 cm2
(C) 4.2 cm2
A liquid with coefficient of volume expansion
(D) 5.3 cm2 is filled in a container of a material
having the coefficient of linear expansion a. If the liquid over flows on heating then (A) 14)
(B)
(C)
(D)
Two iron bars of same length with unequal radii are heated for the same rise in temperature. The linear expansion will be
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(A) more in thin bar.
(C) same for both.
(B) more in thick bar.
(D) less in thick bar.
If
and
are coefficients of linear, superficial and volume expansions of solid,
then
16)
(A)
(C)
(B)
(D)
The length of an aluminium rod is 120 cm at 20 °C. What is its length at 80 °C, if coefficient of linear expansion of aluminium is (A) 130.18 cm
17)
(D) 100.18 cm
(B)K cal/ms K
(C) Watt/m °C
(D) J/m2s°C
Which of the following has minimum coefficient of linear expansion? (A) Gold
19)
(C) 110.18 cm
Which of the following is not the unit of thermal conductivity ? (A) J/ms °C
18)
(B) 120.18 cm
?
(B) Copper
(C) Platinum
(D) Invar steel
The volume of liquid is 830 m3 at 30 °C and 850 m3 at 90 °C. The coefficient of volume expansion of liquid is (A)
20)
(B)
(C)
(D)
One end of a metal rod one metre long is kept in ice and the other end is at 100 °C. What is temperature gradient throughout the rod ? (A) 10 °C/m
21)
(B)100 °C/m
(C) 50 °C/m
(D) 1 °C/m
A metal rod having a coefficient of linear expansion of
has a length of
100 cm at 20 °C. The temperature at which it is shortened by 1 mm is (A) -40 °C 22)
(B)-30 °C
(C) -20 °C
(D) -10 °C
The coefficient of cubical expansion of a solid is the increase in volume per unit original volume at 0 °C per degree rise in ________. (A) pressure
23)
24)
(C) temperature
(D) area
The highest point on Kelvin scale is (A) boiling point of water.
(C) boiling point of alcohol.
(B) triple point of water.
(D) absolute zero.
The motion of gas molecules is mainly (A) Circular
25)
(B) volume
(B) whirlpool type
(C) rotational
(D) translational
The sum of all energies of all molecules in a body is called as _______. (A) kinetic energy
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Heat is transferred between two (or more) systems or a system and its surrounding by virtue of
27)
28)
29)
(A) temperature difference.
(C) amount of heat difference.
(B) material difference.
(D) mass difference.
On Celsius scale, the two fixed points are marked as (A) 0 °C and 232 °C
(C) 0 °C and 100 °C
(B) 32 °C and 100 °C
(D) 100 °C and 180 °C
In the gas equation, PV = RT, V stands for volume of (A) any amount of gas.
(C) one gram of a gas.
(B) one gram mole of gas.
(D) one litre of a gas.
1 litre of an ideal gas at 27 °C is heated at constant pressure so as to attain temperature 297 °C. The final volume is approximately (A) 1.2 litre
30)
33)
(D) JK-1 °C
(B) J kg-1
(C) J kg-1 °C
(D) J-1 kg °C
(C) sea to sky
(B) sea to land
(D) land to land
The slowest mode of transfer of heat is (B)convection
(C) radiation
(D) specific heat
In Newton’s law of cooling, the rate of fall of temperature (B)increases
(C) decreases
(D) doubles
If the temperature in a room is 30 °C, temperature in degree Fahrenheit is (A) 22 °F
36)
(C) J-1K-1 mole-1
(A) land to sea
(A) constant 35)
(B)JK mole-1
Convention currents in air in day time is from
(A) conduction 34)
(D) 2.4 litre
The S.I. unit of latent heat is (A) J-1 kg
32)
(C) 19 litre
The unit of molar specific heat is (A) JK-1 mole-1
31)
(B)1.9 litre
(B) 62 °F
(C) 86 °F
(D) 96 °F
If the temperature on Fahrenheit scale is 140 °F, then the same temperature on Kelvin scale will be (A) 60.15 K
37)
(B) 213.15 K
(C) 333.15 K
(D) 413.15 K
________ amount of heat is required to raise the temperature of 100 g of kerosene from 10 °C to 30 °C (Given: specific heat of kerosene is 0.51 kcal/kg °C) (A) 0.102 kcal
38)
(B) 1.02 kcal
(C) 10.2 kcal
(D) 102 kcal
The metal sphere cools at 1 °C/min, when its temperature is 50 °C. If the temperature of environment is 30 °C, its rate of cooling at 35 °C is
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CONTACT: 9821131002/9029004242 (B)0.5 °C/min
(C) 0.75 °C/min
(D) 0.4 °C/min
How much should the pressure be increased in order to decrease the volume of a gas by 10% at a constant temperature? (A) 7%
40)
(B)8%
(C) 10%
(D) 11.11%
If the pressure of a gas is increased by 20% at constant temperature, the percentage change in its volume is (A) 16.67% decrease
(C) 20% increase
(B) 16.67% increase
(D) 20% decrease
❖ Answer To Multiple Choice Questions 1. (A)
2. (B)
3. (D)
4. (B)
5. (C)
6. (B)
7. (A)
8. (B)
9. (C)
10. (C)
11. (A)
12. (A)
13. (B)
14. (A)
15. (A)
16. (B)
17. (D)
18. (D)
19. (C)
20. (B)
21. (B)
22. (C)
23. (B)
24. (D)
25. (C)
26. (A)
27. (C)
28. (B)
29. (B)
30. (A)
31. (B)
32. (B)
33. (A)
34. (C)
35. (C)
36. (C)
37. (B)
38. (A)
39. (D)
40. (A)
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