Thermal Expansion Questions and Answers

A sphere of diameter 7 cm and mass 266 5 g floats in a both of liquid As the temperature is raised the sphere just sinks at a temperature of 35 C If the density of the liquid at 0 C is 1 527 g cm then the P coefficient of cubical expansion of the liquid is 3 4 b 0 00083 d 0 00010 C a 0 0043 C c 0 00025 C 5 Pressure Ver

Q 1 6 kJ The value of adiabatic exponent A metal ball of mass m is heated by means of a 18 watt heater in a room at 20 C The temperature of ball becomes steady at 50 C Assuming Newton s law of cooling calculate the rate of loss of heat in watt to the surrounding when the ball is at 30

Q 101 A vessel is filled with a gas at one Q 101 atmospheric pressure At the same temperature the mass of that gas is increased by 25 the pressure of gas in the vessel will be 1 0 5 atm 3 1 atm 2 0 75 atm 4 1 25 atm for at 1 0 5 atm 3 1 atm 2 0 75 atm 4 1 25 atm te 25

The temperature of a wire of length 1 metre and area of cross section rod is not allowed to increase in length the force required will be A 10 N B 10 N C 10 N D 10 N is increased from 0 C to 100 C It and Y 10 N m 1cm 10 C

Fig 9 15 mild steel wire of length 1 0 m and cross sectional area 0 50 x 10 cm stretched well within its elastic limit horizontally between two pillars A mass of gis suspended from the mid point of the wire Calculate the depression at the m

A Carnot engine has an efficiency of 20 When temperature of sink is reduced by 80 C its efficiency is doubled The temperature of source is NCERT Pg 313 me 1 1492 C 2 400 C 3 127 C 4 80 C In the adiabatic expansion of an ideal gas select the incorrect statement NCERT Pg 312 1 There is decrease in temperature of the gas 2 There is decrease in internal energy of the gas 3 The work done is positive 4 The work done by gas is equal to heat supplied An ideal gas has initial volume V and pressure P To triple its volume the minimum work done will be in 1 Isothermal process 2 Adiabatic process 3 Isobaric process 4 Equal in all process An ideal gas of adiabatic exponent is expanding at constant pressure The ratio of dQdU dW is Symbols have their usual meanings NCERT Pg 309 1 7 5 1 2 7 2 5 3 2 1 1 4 7 5 2 12 A refrigerator is to maintain etables kept inside at 2 C If room temperature is 27 C then coefficient of performance of refrigerator is NCERT Pg 322 1 10 2 9 3 11 4 8 1 The given figure shows the pressure temperature P T diagram for a fixed mass of an ideal gas undergoing cyclic process ABCA The corresponding pressure volume P V graph 3 NCERT Pg 312 14 Which of the following is incorrect NCERT Pg 305 1 If two systems A and B are in thermal equilibrium with system C separately then A and B will be in thermal equilibrium 2 Zeroth law of thermodynamics defines temperature 3 Temperature does not determine the direction of flow of heat when two bodies are placed in thermal contact 1 4 Internal energy of an ideal gas depends on the state of the system 3 2 15 Which of the following graph does not belong to isothermal process for an ideal gas NCERT Pg 311 P 4 P P V P B PV constant V V 2 4 P O V A B F

A U tube has a liquid at 0 C and 100 C in the two limbs The heights of the liquid colum are 20 cm and 22 cm respectively The coefficient of real expansion of the liquid is 1 0 5 1030 C 1 10 3 0 C 21 100 C 2 3 4 1 10 15

1 A body cools from 80 C to 70 C in 12 minutes and from 70 C to 60 C in time t The value of t is temperature of the surrounding is 40 C 1 13 8 minute 2 16 8 minute 3 18 8 minute 4 20 8 minute

The lengths of an iron and a zinc rod at 0 C are 25 55 cm an 25 5 cm respectively At what temperature will their lengths equal Coefficients of linear expansion of iron and zinc a 10 10 6 C and 30 10 6 C 1 respectively 98 C appro

41 Compressed air is contained in a cylinder at room temperature It suddenly start leaking through a hole Which of the following correctly describes the behaviour of the gas coming out A There is no change in its temperature B It gets cooler C It becomes hotter D It may get cooler or become hotter depending on the humidity in the in

How much heat energy must be added to a 7 6 cm diameter copper sphere to raise its temperature from 50 C to 130 C Express your answer with the appropriate units H

When placed in air at 30 C the temperature of a body decreases from 60 C to 50 C in ten minutes After next ten minutes its temperature will be Question Type Single Correct Type 1 2 08 Physics 3 4 Less than 40 C 40 C More than 40 C English Not definite

Which one of the following statements is wrong 1 Young s modulus for a perfectly rigid body is zero 2 Bulk modulus is relevant for solids liquids and gases 3 Rubber is less elastic than steel 4 The Young s modulus and shear modulus are relevant for solids

In a thermodynamical process pressure of fixed mass of gas is changed in such a way that the gas molecules give out 30 J of heat and 10 J of work is done on the gas If the internal energy of the gas was 40 J the final internal energy will be Question Type Single Correct Type 1 2 3 4 zero 80 J 20 J 20 J 7

The coefficient of linear expansion of crystal in one direction is a and that in every direction perpendicular to it a2 The coefficient of cubical expansion is Question Type Single Correct Type 1 2 3 a a 2a a a 2a

is attached to one end of a massless string length the other end of which is attached to a fixed support O The mass swings around in a vertical circle as shown in figure The mass has the minimum speed u 5g necessary at the lowermost point of the circle to keep the string from going slack u 5gl If you cut the string when it is making angle 0 as shown in the figure with vertical line through centre O of the circle the resulting projectile motion of the mass has its maximum height located directly above the center of the circle Find the value of 10 cos 0

The work done in blowing a soap bubble of radius R is W at room temperature Now the soap solution is heated From the heated solution another soap bubbl of radius 2R is blown and the work done is W Then W2 0 W2 4 W W2 W

C4 If two rods of length L and 2L having coefficient 24 of linear expansion a and 2a respectively are connected end to end The average coefficient of linear expansion of composite rod is 1 3 3 25 5 2 a 2 4 4

The speed of a transverse wave going on a uniform wire having length of 50 cm and mass 5 0 gram is 120 m s The area of cross section of the wire is 0 5 mm and its Young s modulus is 8 x 10 N m Find the extension in mm of the wire over its natural length 50 cm TII 72I 5 0 IIH G TH ga HHU az uz farfa yG HJUZY A H120 m s a 0 5 mm AC N GAZY 8 10 N m Ah 92 DR GAR Mm ma AA

19 33 A monoatomic ideal gas initially at temperature T is enclosed in a cylinder fitted with a frictionless piston The gas is allowed to expand adiabatically to a temperature T by releasing the piston suddenly If L and L are lengths of the gas column before and after expansion respectively then T T is given by 2 2 3 5 3 2 3 a TC 4 L b 4 L2 5 3 eye 2 d c

The temperature of a liquid in a Toricelli barometer with large base vessel slightly changes by AT and the atmosphere pressure remains constant at that place The height h of the liquid column in the barometer changes by Ah If the coefficient of volume expansion of the liquid is y and we don t neglect the expansion of the glass tube then Ah A yhAT C AT B HAT 3 D a value depending on a of glass

Qc Variation of radiant energy emitted by sun filament of tungsten lamp and welding are as a function of its wavelength is shown in figure Which of the following option is the correct match Ex T3 T T A 1 Sun T tungsten filament T welding arc T3 2 Sun T2 tungsten filament T welding arc T3 3 Sun T3 tungsten filament T welding arc T 4 Sun T tungsten filament T3 welding arc T Pag

A composite metal bar of uniform section is made up of length 25 cm of copper 10 cm of nickel and 15 cm of aluminium Each part being in perfect thermal contact with the adjoining part The copper end of the composite rod is maintained at 100 C and the aluminium end at 0 C The whole rod is covered with belt so that no heat loss occurs at the sides If Kcu 2KAI and KAI 3KNi then what will be the temperatures of Cu Ni and Ni Al junctions respectively Cu Ni Al 100 C 1 incorrect attempts 83 33 C and 20 C 50 C and 30 C 0 C 23 33 C and 78 8 C

14 The temperature co efficient of resistance of a wire 21 1 at 0 C is 0 00125 C 1 At 25 C its resistance is one ohm The resistance of the wire will be 1 2 ohm at 1 225 K 3 260 C 2 190 C 4 185 K

When the temperature of a rod increases from t to t AT its moment of intertia increases from I to 1 Al If a be the coefficient of linear expansion AI of the rod then the value of is A B C 20 At a At a At 2

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are y and Y2 respectively If the coefficient of linear expansion of the vessel A is a the coefficient of linear expansion of the vessel B is A B C 07172 71 72 71 72 20 71 72 0 3

A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart The diameter of the rim and the rion ring are 5 243 m and 5 231 m respectively at 27 C To what temperature should the ring be heated so as to fit the rim of the wheel A B C 218 C 118 C 318 C O 418 C D

Two spheres of the same material have the same radius but one is hollow while the other is solid Both spheres are heated by same temperature Then D The solid sphere expands more The hollow sphere expands more Expansion is same for both Nothing can be said about their relative expansion if their masses are not given

Q 3 What effect the following changes will makes to the range sensitivity and responsiveness of a mercury in glass thermometer a Increase in size of the bulb b Increase in diameter of the capillary bore c Increase in length of the stem Har of thicker glass for the bulb

Q 1 In a temperature scale X ice point of water is assigned a value of 20 X and the boiling point of water is assigned a value of 220 X In another scale Y the ice point of water is assigned a value of 20 Y and the boiling point is given a value of 380 Y At what temperature the numerical value of temperature on both the scales will be same

The work done by battery to transfer a 32 charge of 8 10 18 C on a condenser of capacity 100 micro farad is 1 16 10 2 J 2 3 1 10 26 J 3 64 10 2 J 4 32 10 2 J 100 Heav RT 8 x 10 18 C 1 16 10 2 J 2 3 1 10 26 J 3 64 10 2 J 4 32 10 2 J

S T very long conduit of inner circular cros thermal conductivity of 1 W m K passes a hot fluid which maintains the inner surface at T 50 C The outer surfaces of square cross section are insulated or maintained at a uniform temperature of T 20 C depending on the application Find the shape factor and the heat rate for each case T 1 40 mm T 120 mm T T 2 T2 T

2 Liquid oxygen at 60K is heated to 300 K at constant pressure of 1atm The rate of heating is constant Which of the following graphs represent the variation of temperature with time Temp 1 2 3 Time Temp P F Temp Temp Time Time

6 On heating a liquid of coefficient of cubical expansion y in a container having co efficient of Y 2 linear expansion the level of liquid in the container will For a container of rectangular cross section if y 2 1 Rise 2 Fall

An arrangement consisting of slabs is shown in the figure When system is placed in situation a with temperature difference is maintained between 1 2 equivalent thermal conductivity of system is K and when system is changed to situation b and temperature difference is maintained between 3 4 then equivalent thermal conductivity increases by 20 Find number of slabs in the arrangement P 2k nk n 2 n 2k nk b 4

1 The pressure of a medium is changed from 1 01 x 105 Pa to 1 165 105 Pa and change in volume is 10 keeping temperature constant The bulk modulus of the medium is a 204 8 105 Pa b 102 4 105 Pa 2005 2M d 1 55 x 105 Pa c 51 2 x 105 Pa

1 A solid sphere of radius R acquires a terminal velocity v when falling due to gravity through a viscous fluid having a coefficient of viscosityn The sphere is broken into 27 identical solid spheres If each of these spheres acquires a terminal velocity v when falling through the same fluid the V2 ratio v v equals 2019 Main 12 April II a 9 b 1 27 d 27 c 1 9

4 40 C 19 A P V diagram for a thermodynamic process is shown in the figure If T T then choose the correct option during the process PA 1 Temperature continuously increases 2 Temperature continuously decreases Temperature first increases then decreases 4 Can t predict temperature variation with given

3 Evaporation 4 All of these 8 Volume versus temperature graph of two mole of helium gas is as shown in figure The ratio of change in internal energy and the work done by the gas in process 1 2 is 1 52 7 2 3 2 4 32 73

If the cost of energy is 0 24 per Kwh how much would it cost to heat a pool of length 12 metres width 9 metres depth 1 5 metres from 15 degrees celsius to 27 degrees celsius Hint the specific heat capacity of water is 4 184 Joules 642 2464 442 2464

42 Hot water at 50 C is routed from one building in which it is generated to an adjoining uilding in which it is used for space heating Transfer between the buildings occurs in a eel pipe k 60 W m K of 100 mm outside diameter and 8 mm wall thickness During e winter representative environmental conditions involve air at T 5 C and V 3 m s cross flow over the pipe a If the cost of producing the hot water is 0 10 kWh what is the representative daily cost of heat loss from an uninsulated pipe to the air per meter of pipe length The convection resistance associated with water flow in the pipe may be neglected b Determine the savings associated with application of a 10 mm thick coating of urethane insulation k 0 026 W m K to the outer surface of the pipe

7 An anisotropic material has coefficient of linear thermal expansion a a2 and a3 along x y and z axis respectively Coefficient of cubical expansion of its material will be equal to 1 a a 03 3 30 202 03 2 a 2a 303 a a 3 4 2

Test 4 Code A 29 When the temperature of a rod increases from T to T AT its moment of inertia increases from to Al If a be the coefficient of linear expansion of 30 rod then value of 1 20AT 3 CAT 2 Al is 2 CAT AT a 4 Water flows steadily through horizontal ning of 36 A mer drople proces 1 4 3 4 37 The aw simple oscillan

Statement 1 The temperature dependence of resistance is usually given as R R 1 ast The resistance of a wire changes from 100 2 to 150 2 when its temperature is increased from 27 C to 227 C This implies that 2 5 x 10 C Statement 2 R R 1 aAt is valid only when the change in the temperature AT is small and AR R R Ro AIEEE 2009 1 Statement 1 is true statement 2 is true Statement 2 is the correct explanation of Statement 1 2 Statement 1 is true Statement 2 is true Statement 2 is not the correct explanation of Statement 1 3 Statement 1 is false Statement 2 is true 4 Statement 1 is true Statement 2 is false

The stress strain graph for a metallic wire is shown at four different temperature T T2 T3 and T4 then Stress T T 4 T3 C T T T3 T4 3 T3 T T T The Bulk modulus for atomicity of gas in Strain 2 T T T3 T4 4 T T T T3 2 gases depends on the

An ideal gas is at initial temperature T and pressure P If pressure changes from P to P dp when temperature changes from T to T dT at constant volume the value of pressure coefficient p varies as shown in graph below The correct graph is P B 1 T L O 1 T L T

The coefficients of linear expansion of steel and brass are 11 x 10 6 C and 19 x 10 6 C respectively If their difference in lengths at all temperatures has to be kept constant is 30 cm their lengths at 0 C should be A 71 25 cm and 41 25 cm B 82 cm and 52 cm C 92 cm and 62 cm D 62 25 cm and 32 25 cm

The reading of brass scale at room temperature is L Above room temperature reading is L and below room temperature reading is L3 then relation between the readings is A L L L3 B L3 L L CI D

An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure The efficiency of the gas cycle is P 3Po B Po A Vo 2Vo V D Question Type Single Correct Type 1 4 21 2 2 21

10 k Gulab Jamuns assumed to be spherical are to be heated in an oven They are available in two sizes one twice bigger in radius than the other Pizzas assumed to be discs are also to be heated in oven They are also in two sizes one twice big in radius than the other All four are put together to be heated to oven temperature Choose the correct option from the following a Both size gulab jamuns will get heated in the same time b Smaller gulab jamuns are heated before bigger ones c Smaller pizzas are heated before bigger ones d Bigger pizzas are heated before smaller ones