Thermal Expansion Questions and Answers

22 A bubble of 8 mole of helium is submerged at a certain depth in water The temperature of water increase by 60 C How much heat is added approximately to helium during expansion a 1000 cal b 7000 cal c 1400 cal d 1500 cal

23 A lake is covered with ice 2 cm thick The temperature of ambient air is 15 C Find the rate of thickening of ice For ice k 4 x 10 4k cal m s C density 9 10 kg m and latent heat L 80 Kilo Cal Kg

Two rods one of aluminum and the other made of steel having initial length and 12 are connected together to form a single rod of length 1 1 The coefficients of linear expansion for aluminum and stee are da and as respectively If the length of each rod increases by the same amount when their temperature 1 are raised by t C then find the ratio 1 1 0 5 da 05 05 5

1 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 vessel A is a The coefficient of linear expansion of the vessel B is a C ay112 Y y 2 Y Y2 3 a b Y Y 2a d Y 1 a 3

A metal rod of silver at 0 C is heated to 100 C Its length is increased by 0 19 cm Coefficient of cubical expansion of the silver rod is Lo 1 m 5 7 x 10 5 C 0 63 x 10 5 C 1 9 10 5 C 16 1 x 10 5 C

Assume that specific heat capacity of a material increases with increase in temperature If equal amount of the substance is mixed in isolation at two different temperatures T K and T K T T then the equilibrium temperature will be 1 Greater than 2 Lesser than 3 T T 2 T T 2 2 T T 2 T DOUBT S T ST Sp S Ads rum T way thus ter

Rank the energy savings potential of the following EE technologies systems from highest to lowest Discuss the expected performance of a building which integrates two or more of the following systems Underfloor Air Distribution Systems Chilled Beams High Performance Building Envelopes Radiant heating and Cooling Variable Refrigerant Flow Ground Source Heat Pumps and Thermal Energy Storage State your assumptions

1 A uniform cylindrical rod of length L and radius r is made from a material whose Young s modulus of elasticity equals Y When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F its length remains unchanged The coefficient of volume expansion of the material of the rod is nearly equal 2019 Main 12 April II b 6F nr YT d F 3 r YT to a 9F r YT 3F Tr YT Ses BF

Two cylinders of equal size are filled with equal amount of ideal diatomic gas at room temperature Both the cylinders are fitted with pistons In cylinder A the piston is free to move while in B position is fixed When same amount of heat is suplied to both the cylinders the temperature of the gas in cylinder A raises by 30 K What will be the rise in temperature of the gas in cylinder B a 42 K b 30 K 20 K 20 K d 56 K c c

13 The change in volume in cm of a metal sphere of radi 10 cm when its temperature is increased from 10 C 60 C is Given that coefficient of volume expansion the sphere is 6 9 10 5 C a 2 3 b 4 6 T c 6 9 T d 9 2 T

An uranium 235U fission reaction produces 92 216 MeV The amount of 235U required to run a 92 100 MW nuclear power plant for a day with 100 efficiency is 1 0 01 kg 3 0 1 kg 2 1 kg 4 0 001 kg

Steel wire of length L at 40 C is suspended from the ceiling and then a mass m is hung from its free end The wire is cooled down from 40 C to 30 C to regain its original length L The coefficient of linear thermal expansion of the steel is 105PC Young s modulus of steel is 10 N m and radius of the vire is 1 mm Assume that L diameter of the wire Then the value of m in kg is nearly 2011

PHYSICS 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 A along y axis is Raat 4R B A along x axis is ast 3m C B along x axis is Rast D B along y axis is zero

21 a An oil trucker loaded 40000 liters of certain fuel during his travel He reached the destination where the temperature was 20 C lower than that of the temperature at the starting point The coefficient of the volume expansion of the fuel is 8 225x10 4 C How much load he delivered at the destination point

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats y It is moving with speed v and is suddenly brought to rest Assuming no heat is lost to the surroundings its temperature increases by 1 7 1 2 y 1 R Mv K 2 Y Mv K 27R 3 My K 2R 7 1 Mv K 4 AIEEE 2011 2R partition fitted with a valye One part is filled with an

A rod of length 20 cm is made of metal It expands by 0 075cm when its temperature is raised from 0 C to 100 C Amother rod of a different metal B having the same length expand by 0 45 cm for the same change in temperature A third rod of the same length is composed of two parts one of metal A and the other of metal B This rod expands by 0 060 cm for the same change in temperature The portion made of metal A has the length 1 20 cm 2 10 cm AIPMT 91 3 15 cm 4 18 cm

The thermal conductivity of brick is 1 7 W m K and that of cement is 2 9 W m K What thickness of cement will have same insulation as the brick of thickness 20 cm Assuming their area to be same

3 7 x 10 J 4 A diatomic ideal gas is used in a Carnot engine as the working substance If during the adiabatic expansion part of t cycle the volume of the gas increases from V to 32 V the efficiency of the engine is AIEEE 201 1 0 5 2 0 75 3 0 99 4 0 25

Four metalic conductors having different shape Sphere cylinder pear lighting conductor an mounted on insulating stands and charged TH one which is best suited to retain the charges fo a longer time is 1 Sphere 3 Pear 2 Cylinder 4 Lightning conduct

A glass cylinder contains mo 100 g of mercury at a temperature of to 0 C When temperature becomes t 20 C the cylinder contains 99 7 g of mercury The coefficent of volume expension of mercury XHE 18 times 10 5 C Assume that the temperature of the mercury is equal to that of the cylinder The coefficent of linear expansion of glass a is A B C D 10 5 C 2 x 10 5 C 3 x 10 5 C 6 10 5 C

Density of a substance at 0 Cis 10 6 g cc and at 100 C is 10 g cc Find the coefficient of linear expansion of solid a 0 0006 C b 0 0004 C c 0 0003 C d 0 0002

3 A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container A massless piston of area a floats on the surface of the liquid covering entire cross section of cylindrical container When a mass m is placed on the surface of the piston dr to compress the liquid the fractional decrement in the radius of the sphere 1 mg 3 Ka 2 mg Ka 3 Ka mg 4 is Ka 3 mg

TWO and 3h 2 are the V2 is 25 A constant force Fo is applied on a uniform elastic string placed over a smooth horizontal surface as shown in figure Young s modulus of string is Y and area of cross section is S The strain produced in the string in the direction of force is a For S b Fo SY L c Fo Fo 2SY d Foy 2S

At some temperature T a bronze pin is a little large to fit into a hole drilled in a steel block The change in temperature required for an exact fit is minimum when only the block is heated both block and pin are heated together both block and pin are cooled together only the pin is cooled

Three uniform rods of lengths l 2l and 3l masses m 2 m and 3 m and coefficient of linear expansion a 2a and 3a are placed in contact on a smooth horizontal surface as shown in figure The temperature of the system is increased by T Which of the following options is are correct Take laT e 1 A C B m m m m 77 m l a 2m 2l 2a B and C shift by equal distance 2e in opposite directions A shifts left by 35 e D shifts right by 777 77 3m 36 3a 49 A and D shift by equal distance 7e in opposite directions

l Question 12 A system of rods is assembled such that each rod has a length and cross sectional area S The mode of heat transfer is conduction and the system is in steady state The temperature of junction A is T and that of C is 2T Thermal conductivities of rods are mentioned in term of k Now answer the following questions D A 2k k 2k B Temperature of junction B is Options a 1 4T b 1 6T c 1 8T d 1 5T I

Two conductors A and Beach of cross section area 5 cm are connected in series Variation of temperature in C along the length in cm is as shown in the figure If thermal conductivity of A is 120 Jim sec C The thermal conductivity of B is 40K J m sec C Find the value of K TA 53 25cm 45 50cm

Question 21 A gaseous mixture initially at 300 K and 2 x 105 N m pressure contains 6 gm of H and 8 gm of He The mixture is expanded four times its initial volume through a isobaric heating process Then it is isochorically cooled until its temperature again become 300 K After that the gas mixture is isothermally compressed to its original volume Work done by complete cycle is Po Vo are initial pressure and volume respectively ong

OPPER An iron bar 10cm in length is kept at 20 C If the coefficient of linear expansion of iron is a 11x10 C then at 19 C it will be 1 11x10 cm longer 3 11x10 cm shorter 2 11x10 cm shorter 4 11 10 cm longer

Following figure shows on adiabatic cylindrical container of volume Vo divided by an adiabatic smooth piston area of cross section A in two equal parts An ideal gas Cp Cy y is at pressure P and temperature T in left part and gas at pressure P2 and temperature T2 in right part The piston is slowly displaced and released at a position where it can stay in equilibrium The final pressure of the two parts will be Suppose x displacement of the piston P T 1 P2 2 P 3 Y P 7 2 Ax P P 2 Y P T

A cylindrical container of radius R and height h is completely filled with a liquid Two horizontal L shaped pipes of small cross section area a are connected to the cylinder as shown in the figure Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions Then the torque due to ejected liquid on the system is h 2 K R 2r h 2 R

A cable that can support a load W is cut into two equal parts The maximum load that can be supported by either part is Question Type Single Correct Type 1 2 3 W 4 W 2 W

A simple seconds pendulum is constructed out of a very thin string of thermal coefficient of linear expansion a 20 10 4 C and a heavy particle attached to one end The free end of the string is suspended from the ceiling of an elevator at rest The pendulum keeps correct time at 0 C When the temperature rises to 50 C the elevator operator of mass 60 kg being a student of Physics accelerates the elevator vertically to have the pendulum correct time The apparent weight in N of the operator when the pendulum keeps correct time at 50 C is 330x Find x Take g 10 m s O O O 2 5 4 2

A balloon is filled with helium at the atmospheric pressure Po The volume of spherical balloon is Vo Afte Po being released the balloon burst at an altitude where the atmospheric pressure is Before bursting 2 the balloon has volume 5V temperature remaining the same If the mass of material of balloon is 4 and density at the time of bursting is po then A Pressure inside the balloon before bursting is P 4 B Pressure inside the balloon before bursting is Po C Maximum stress which balloon can withstand is D Maximum stress which balloon can withstand is 9PoVoPo 16m 3Popovo 8m

A non isotropic solid metal cube has coefficients of linear expansion as 5 x 10 5 C along the x axis and 5 x 10 6 C along the y and the z axis If the coefficient of volume expansion of the solid is C x 10 16 C then the value of C is

Q17 A composite bar of 20mm x 20mm cross section is made up of three flat bars as shown in figure All the three bars are rigidly connected at the ends when the temperature is 20 C determine i the stress developed in each bar when the temperature of the composite bar is raised to 60 C ii the final stresses in each bar when the load of 17 6 kN is applies to the composite bar Es 200 Gpa EAI 80 Gpa as 22 x 10 C aA 11 x 10 C 20 mm STEEL ALUMINIUM STEEL 20 mm 8mm 4 mm 8 mm

An aluminium measuring rod which is correct at 5 C measures the length of a line as 80 cm at 45 C If thermal coefficient of linear expansion of aluminium is 2 50 x 10 5 C the correct length of the line is A 80 08 cm B 79 92 cm C 81 12 cm D 79 62 cm

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0 5 and length 3 m and 1 m respectively Their other ends are fixed on a ceiling as shown in figure angles subtended by copper and steel wires with ceiling are 30 and 60 respectively If elongatic Alc copper wire is Ac and elongation in steel wire is As then the ratio Als Young s modulus for copper and steel are 1 x 1011 N m2 and 2 x 10 1 N m respectively Sleel wire 1 m 60 Block 3 30 Copper wire Cis

8 A steel rod of length 1 m is heated from 25 to 75 C keeping its length constant The longitudinal strain developed in the rod is Given coefficient of linear expansion of steel 12 10 C a 6x10 4 c 6x10 4 b 6x10 5 d zero

Example 20 3 A steel ruler exactly 20 cm long is graduated to give correct measurements at 20 C a Will it give readings that are too long or too short at lower temperatures b What will be the actual length of the ruler when it is used in the desert at a temperature of 40 C a steel 1 2 x 10 5 C Solution a IS

Temperature of nitrogen in a vessel of volume 2 m is 288 K A U tube manometer connected to the vessel shows a reading of 70 cm of mercury level higher in the end open to atmosphere The universal gas constant is 8314 J kmol K atmospheric pressure is 1 01325 bar acceleration due to gravity is 9 81 m s and density of mercury is 13600 kg m The mass of nitrogen in kg in the vessel is

9 The coefficient of linear expansion of steel and brass are 11 x 10 6 C and 19x106 C respectively If their difference in lengths at all temperatures has to kept constant at 30 cm their lengths at 0 C should be a 71 25 cm and 41 25 cm c 92 cm and 62 cm FTIT b 82 cm and 52 cm d 62 25 cm and 32 25 cm

A furnace wall consists of 100 mm thick refractory brick and 800 mm thick insulating fire brick separated by an air gap The outside wall is covered with a 20mm thick ness of plaster The inner surface of the wall is at 1500 C and the ambient temperature is at 26 c Calculate the rate at which heat is lost per m of the wall surface The heat transfer coefficient of the ambient air is mentioned to be 22W m K and the air gap resistance to the heat flow is given as 0 16 K W The thermal conductivity of refractory brick insulating fire brick and plaster are 1 5 0 25 and 0 13 W m K respectively Also calculate the interface temperatures of the walls 1100 c RF Bri Insulating Fire Brick R Eins 26 C h 22W m K

Forces of 100 N each are applied in opposite directions on the upper and lower faces of a cube of side 20 cm The upper face is shifted parallel to itself by 0 25 cm If the side of the cube were 10 cm then the displacement would be O 0 25 cm O 0 5 cm O 0 75 cm O 1 cm

If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron the ratio of the force developed in the copper bar to the iron bar of identical lengths and cross sections when heated through the same temperature range Young s modulus for copper may be taken equal to that of iron is O 3 2 2 3

A thermally insulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at constant power P This leads to an increase in the absolute temperature T of the metal with time t as T t T 1 a t to where a to and To are constants The heat capacity Cp T of the metal is A 4P aTo

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 the length of gas column before and after expansion respectively Then T T is given by 18

A wall made up of two layer X and Y The thickness of the two layers is the same but materials are different The thermal conductivity of X is thrice than that of Y In thermal equilibrium the temperature difference between the two ends is 56 C Then the difference of temperature across wall X is X 3K H A 21 C B 35 C Y K t MY

13 A solid uniform metal bar of diameter Dand length Lis hanging vertically from its upper end The elongation of the bar due to self weight is a Proportional to L and inversely proportional to D b Proportional to L2 and inversely proportional to D c Proportional to L but independent of D d Proportional to L2 but independent of D FOF 00051

10 A A steel scale is to be prepared such that the millimeter intervals are to be accurate within 6x10 mm The maximum temperature variation from the temperature of calibration during the reading of the millimeter marks is linear coefficient of expansion for steel is given as a 12 10 C 1 4 0 C 3 5 0 C 4 5 5 C 2 4 5 C When a bimetallic strip is heated it