Thermal Expansion Questions and Answers

If two metallic plates of equal thicknesses and thermal conductivities K and K are put together face to face and a common plate is constructed then the equivalent thermal conductivity of this plate will be MP PMT 1991 al a c K K K K K K 2 K K K K b d 2 K K K K K K 2 2K K

2 Assertion A Kinetic theory deals with bulk systems in terms of macroscopic quantities such as temperature internal energy entropy etc Reason R Kinetic theory and statistical mechanics interpreted these quantities in terms of the properties of the molecular constituents of the bulk system

Graphs give the temperature along an x axis that extends directly through a wall consisting of three layers with different nonzero and finite coefficient of thermal conductivities The air temperature on both sides of the wall are different and uniform Out of the situations as shown by the graphs which is are impossible T A A TA C ABC ABC Digital Cla B 1 D AB C X LI 1 ABC X

10 Consider the situation shown in figure The force F is equal to the m g 2 If the area of cross section of the string is A and its Young s modulus Y find the strain developed in it The string is light and there is no friction anywhere 1 3 m g 2m m AY m m m g 2m m 2AY m m m m g m m 2AY m m 4 None of these 10 fer effe affufa fram affer mg 2f Aegean given 1 3 m m g 2m m AY m m m g 2m m 2AY m m 4 m mg m m 2AY m m

A water cooler of storage capacity 120 liters can cool water at a constant rate of P within closed circulation system as shown schematically in the figure the water from the coo is used to cool an external device that generates constantly 3Kw of heat thermal road 1 temperature of water fed into the device cannot exceed 30 C and the entire stored 120 lit of water is initially cooled to 10 C The entire system is thermally insulated The minimu value of P in watts for which the device can be operated for 3 hours is Specific heat of water is 4 2KJKg K 1 and the density of water is 1000kgm Cooler HOT Device

A steel bolt of cross sectional area A 5 x 105 m is passed through a cylindrical tube made of aluminium Cross sectional area of the tube material is A 10 m and its length is 50 cm The bolt is just taut so that there is no stress in the bolt And temperature of the assembly is increases through A0 10 C Given coefficient of linear thermal expansion of steel a 10 5 C Young s modulums of steel Y 2 10 N m Young s modulus of Al Y 10 1 N m2 coefficient of linear thermal expansion of Al a 2 x 10 C 29 The compressive strain in tube is A 10 C 2 10 B 5 x 10 5 D 10

Q4 An ideal gas expands isothermally from a volume V to V and then compressed to original volume V adiabatically Initial pressure is p and final pressure is p3 The total work done is W Then 2004 A P3 P1 W 0 B P3 P1 W 0 D P3 D P3 P W 0 C P3 P1 W 0

Two non mixing liquids of densities p and no n 1 are put in a container The height of each liquid is h A solid cylinder of length L and density d is put in this container The cylinder floats with its axis vertical and length pL p 1 in the denser liquid The density d is equal to NEET 2016 1 1 n 1 p p 2 1 n 1 p p 3 2 n 1 p p 4 12 In Uplo

Two resistors of resistance Rand 3R have thermal coefficients of resistance a and 2a respectively Equivalent thermal coefficient of resistance for the combination connected in parallel is O O 5 4 5 7 5 7 3

A light wire of length L area of cross section A is hanging from fixed support If a mass M is suspended from its free end then strain produced in the wire will be symbols have their usual meaning 1 3 Mg 2Y A 2Mg YA 2 Mg YA 4 Zero

A 5 liter glass vessel is filled to its brim with water The coefficient of cubical expansion of water is 1 3 10 C and coefficient of volume expansion of glass is 80 106 C The temperature is increased by 20 C How much water would overflow A 5 cc B 8 CC c 10 cc D 13 cc

3 Q 15 If the length of a cylinder on heating increases by 2 the area of its base will increase by 1 0 5 3 1 long string having 2 2 4 4 cross sectional ar

Initially container was full When temperature change by AT volume of liquid volume of container V V 1 AT Vc Vo 1 Ye AT So overflow volume of liquid relative to container AV V Vc AV V YLYC AT So coefficient of apparent expansion of liquid w r t container f Yapparent YL Yc In case of expansion of liquid container system level of liquid rise YLYC Clevel of liquid fall Increase in height of liquid level in tube when bulb was initially not completely filled OF A LIQUID IN A CONTAINER h volume of liquid area of tube Vo 1 YLAT Ao 1 2agAT ho 1 Y 2as AT h h 1 2 s AT where h original height of liquid in container WST a linear coefficient of expansion of container 1 2017 AV VO x 1

Inner surface of a cylindrical shell of length 1 and of material of thermal conductivity k is kept at constant temperature T and outer surface of the cylinder is kept at constant temperature T such that T T as shown in figure Heat flows from inner surface to outer surface radially outward Inner and outer radii of the shell are R and 2R respectively Due to lack of space this cylinder has to be R replaced by a smaller cylinder of length inner and outer radii and R respectively and thermal 4 conductivity of material nk If rate of radial outward heat flow remains same for same temperatures of inner and outer surface i e T and T then find the value of n T 7 0 0 4

6 A black body at 227 C radiates heat at the rate of 7 cals cm s At a temperature of 727 C the rate of heat radiated in the same units will be AIPMT Prelims 2009 2 112 4 60 1 50 3 80

The value of coefficient of volume expansion o glycerin is 5 x 10 4K 1 The fractional change in the density of glycerin for a rise of 40 C in it temperature is Re AIPMT 2015 1 0 010 3 0 020 2 0 015 4 0 025

aluminium sphere has a diameter of exactly 25 04 mmat it s temperature of 100 C The sphere is placed on top of the ring and two are allowed to come to thermal Sec Sr Super60 All Space for rough work Sri Chaitanya IIT Academy 13 06 2021 Sr Super60 All Jee Adv 2018 P1 GTA 09 Q P equilibrium no heat being lost to the surrounding The sphere just passes through the ring at the equilibrium temperature Find the ratio Given a 696x105 C a 25x10 5 C Page 7 maphere ming

3 The relative density of a metal may be found by hanging a block of the metal from a spring balance and nothing that in air the balance reads 5 00 0 05 N while in water it reads 4 00 0 05 N The relative density would be quoted as a 5 00 0 05 b 5 00 11 c 5 00 0 10 d 5 00 6

clamped rigidly at its ends at temperature to when the temperature t is increased the expanding bar will bow out as shown above If the bowing is not too large a fair first approximation to the shape of the bar is two equal straight segments in the form of a wide V What is the arch of the bow as a function of t This is the distance between the corner of the V and the straight line that represents the form of the bar at to

A certain gas is taken to the five states represented by dots in the graph The plotted lines are isotherms Order of the most probable speed V of the molecules at these five states is P V Pat Pat 4 Pat 5 A Vrat3 Vpat1 V2 Vp V C Vat3 Vpat2 Vpat4 Vpat1 Vpats B Vratt Vrat2 Vrata Vat4 Vpats D Insufficient information to predict the result

A tapered circular bar of length is rigidly fixed at both the ends Diameter of bar at one end is D and other end is d The temperature of the bar is raised by AT The modulus of elasticity and linear DECAT d expansion coefficient of material are E and a respectively If is 3 unit then the maximum thermal stress induced in the bar when its temperature is raised in the given unit will be d D SKIPPE

Two thin rods of length I and 12 at a certain temperature are joined to each other end to end The composite rod is then heated through a temperature The coefficients of linear expansion of the two rods are a and a respectively Then the effective coefficient of linear expansion of the composite rod is A A A 2 B a az C 1 1 0 1 1 D 1 0 10 1 1

Correct relation between three coefficients of a B 7 thermal expansion O a B y 03a 28 y 0 a 31 2 3 Oy B a

B 19 A constant force F is applied on a uniform elastic strig placed over a smooth horizontal surface as shown in Figure Young s modulus of string is Y and area of cross section is A The strain produced in the string in the direction of force is 1 2 3 FOY Fo AY F 2 AY

The ratio of lengths of two rods is 1 2 and the ratio of coefficient of expansions is 2 3 The first rod is heated through 60C Find the temperature through which the second rod is ta be heated so that its expansion is twice that of first is

A bimetallic strip of brass and steel each having thickness of 1 cm is kept at 20 C The strip bends with brass on outer side The radius of curvature of curved surface is abrass 18 10 6 C a steel x 12 10 6 C

Two rods of lengths L and L are made of materials having coefficients of linear expansion a and az respectively If L L2 is independent of temperature which of the following relations is correct 1 L L 2 L L 0 0102 3 L 01 L 02 4 None of these

151 If the same amount of heat is supplied to two spheres of the same material having the same radius one is hollow and the other is solid then 1 the expansion in hollow is greater than the solid 2 the expansion in hollow is the same as that in solid 3 the expansion in hollow is lesser than the solid 4 the temperature of both must be the same as each other

A semi circular disc of radius R is placed on a smooth horizontal surface Figure shows top view of this If temperature is increased by At then displacement of coefficient of linear expansion is a A B C D A along y axis is Ra At A along x axis is 4R 3 77 al B along x axis is Ra At B along y axis is zero B

A one meter long tube open at one end with a movable piston at the other end shows resonance with a fixed frequency source a tuning fork of frequency 340 Hz when the minimum tube length is 25 5 cm The speed of sound in air at the temperature of the experiment is The edge effects may be neglected 1 324 16 m s 2 320 m s 3 345 m s 4 346 8 m s

When a known resistance 8 Qand conductor at 25 Care connected in the right and left gaps of a meter bridge respectively the balancing length is 40cm If the temperature of the conductor is increased to 100 C the balancing length becomes 50cm The temperature coefficient of resistance of the conductor is A 0 008 C B 0 08 C C 0 005 C

9 A cube of a substance of coefficient of cubica expansion y is floating in a liquid of coefficient c cubical expansion Y Y2 such that 50 c its volume is inside the liquid If temperature c the system is now increased the percentage o volume of cube inside the liquid may be 1 50 2 52

Six identical metallic rod as joined together in a pattern as shown in the figure Points A and D are maintained at temperature 60 C and 240 C The temperature of the junction B will be 1 2 A Question Type Single Correct Type 3 120 C 150 C B 60 C C D

a At 20 C the volume of a copper sphere is 40 cm The coefficient of linear expansion of copper is 24 x 10 6 K 1 If the final volume is 40 5 cm what is the final temperature of the er sphere 3 marks

When two different thermometers A and B a re in contact with an object at equilibrium t he length of the mercury column is found to be 3 cm and 6cm respectively When they ar e in contact with another object the length of mercury thread of A is increased by 3 cm Then the length of the mercury thread of the thermometer B is cm 12 8 15 10

In a flask made of glass a a spherical part is fully filled with a liquid y Y If temperature is raised by A8 what will be height of liquid Column in the cylindrical neck Initially spherical part has volume V and area of neck is A

Which of the following statements regarding superconductors is are true 1 The mechanism for Copper based superconductors Cuprates can be explained by electron phonon interaction II The mechanism for superconducting hydrides can be explained by electron phonon interactions III To date the binary hydrides can only become superconducting under very high pressures IV To date the highest critical temperature for Cuprates is 40 Kelvins I and II I and IV II and IV I and III I and IV

l 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 30 cm far from the hotter end Also calculate the temperature gradient n l

A steel wire of cross section 1mm is heated at 60 C and tied between two ends firmly The co efficient of linear expansion for steel is a 1 1x10 5 C and Young s modulus Y 2 10 Pa The change in tension in the wire when temperature becomes 30 C is 1 44N 2 55N 3 66N 4 77N

3 A copper cup of 100 cm capacity is fully filled with glycerin at 25 C What is the required temperature to spill out the 2 52 cm of glycerin from the cup the coefficient of volume expansion of glycerin is 5 1 10 C and the coefficient of linear expansion of copper is 17 10 C a 75 C b 65 C c 70 C d 45 C

1 The frequency of vibration of H2 molecule is 1 32X10 Hz a Find the relative populations of v 0 1 2 3 and 4 vibrational states at 5000K b Can the popiulations of the v 2 and v 3 states ever be equal if so at what temperature does that occur

9 15 A cylindrical metal rod of length Lo is shaped into a ring with a small gap as shown On heating the system X 1d Xx decreases r and d increase x and r increase d decreases Xx r and d all increase Data insufficient to arrive at a conclusion

The tube open at both ends as shown in the figure is completely filled with a liquid The liquid level does not change in the tube with rise in the temperature Let y coefficient of volume expansion of the liquid and a coefficient of linear expansion of the material of the tube Which of the following is correct relation between y a A y a C y 3a B y 2a D y 0

A steel wire whose length is 130 cm and whose cross section area is 9 50 x 10 7 m is heated to an average temperature of 830 C and stretched tout between two rigid supports What tension is developed in wire whe it is cooled to 20 C Y 2 10 N m a 11 x 10 6 C 1200 N 1700 N 2100 N Zero

The filament of a light bulb has a surface area 64 mm The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far At night the light bulb is observed from a distance of 100 m Assume the pupil of the eyes of the observer to be circular with radius 3 mm Then Take Stefan Boltzmann constant 5 67 x 10 8 Wm 2K 4 Wien s displacement constant 2 90 10 m K Planck s constant 6 63 10 34 Js speed of light in vacuum 3 00 x108 ms a power radiated by the filament is in the range 642 W to 645 W b radiated power entering into one eye of the observer is in the range 3 15 10 8 W to 3 25 x 10 8 W c the wavelength corresponding to the maximum intensity of light is 1160 nm d taking the average wavelength of emitted radiation to be 1740 nm the total number of photons entering per second into one eye of the observer is in the range 375 x 1011 to 3 85 x 1011

Show that the coefficient of real expansion of liquid gamma R and the coefficient of apparent expansion of the liquid gammaA are equal In case of 2 dimensional motion one dimensional accelerated motion is possible Explain with a example Mass of 10 CC water at 0 c and 4 c are 9 998 gm and 10 gm respectively calculate the expansion coefficient of water in this temperature

a 9 kg b 0 5 kg c 1 5 kg Two rods A and B of identical dimensions are at temperature 30 C If A is heated upto 180 C and B upto T C then new lengths are the same If the ratio of the coefficients of linear expansion of A and B is 4 3 then the value of T is a 230 C b 270 C c 200 C 2019 Main 11 Jan II d 250 C

The coefficient of volume expansion of a liquid is 49 10 5 K Calculate the fractional change in its density when the temperature is raised by 30 C 7 5 x 10 2 3 0 10 O 1 5 x 10 1 1 x 10

A cylindrical metal rod of length Lo is shaped into a ring with a small gap as shown On heating the system X d r x decreases r and d increase x and r increase d decreases x r and d all increase Data insufficient to arrive at a conclusion

1 A lamina copper is 100 cm long and 15 cm broad at 273 K The area of cross section increases by 2 cm at 100 C What will be the coefficient of linear expansion of sheet material a 10 6 C c 6 6 x 10 6 C b 2 x 10 6 C d 5 x 10 6 C