Thermal Expansion Questions and Answers

34 A U tube is filled with mercury Hg The two limbs are maintained at 0 C and 100 C and the heights of the two columns are 100 cm and 101 8 cm Find the real coefficient of cubical expansion of mercury Expansion of the limb may be neglected A 9 10 5 C C 27 10 5 CEs gnivor el nico 5 B 18 10 5 C D 36 10 5 C

3 0 6 x 10 5 C 4 0 75 x 10 5 C 17 Coefficient of linear expansion of a vessel completely filled with Hg is 1 x 10 5 C If there is no overflow of Hg on heating the vessel then coefficient of cubical expansion of Hg is 1 4 10 5 C 2 3 10 5 C 3 3 10 5 4 Data is insufficient

An anisotropic material has coefficients of linear thermal expansion a2 and a3 along x y and z axis respectively Coefficient of cubical expansion of its material will be equal to a 2a 3a3 O 0 03 3 3a 2a2 a3 a a a3

A clock that keeps correct time at 20 C is subjected to 40 C If coefficient of linear expansion of the pendulum is 12x10 C how much time will gain or lose 1 10 3 s day 2 20 6 s day 3 5s day 4 20 min day CHEMISTRY An ionic compound has a unit cell consisting of A ions at the corners of a cube B ions on the

5 Three rods formed an equilateral triangle ABC at 0 C Rods AB and AC have same coefficient of expansion a and rod BC has a If temperature of the system is increased by At C what is the change in angle 0 formed by rods AB and AC a A0 2 a At 3 b 40 a At 3 c a 5 d 2 a

Inner surface of a cylindrical shell of length and of material of thermal conductivity k is kept at constant temperature T and the 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 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 replaced by a smaller cylinder of length inner and outer radii and R respectively and thermal conductivity of material nk If rate of radially outward heat flow remains same for same temperature of inner and outer surface i e T and T then find the value of n R 2 8 T 010 42R

2 The apparent coefficient of expansion of a liquid when heated in copper vessel is C and when heated in silver vessel S If A is the coefficient of linear expansion for copper the coefficient of linear expansion for silver is A B C C S 3A 3 S 3A C D C 3A S 3 C S 3A 3

the ratio of lengths radii and Young s modulus of steel and brass wires in the figure are a b and c respectively then the corresponding ratio of increase in their lengths would be A C 2a c b 2ac b Steel M Brass 2M B D 3a 2b c 3c 2ab

82 An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure The efficiency of the cycle is C C C 3Po Po B A Vo b 212 C D 2V0 V 0 16 8 d 62 3

16 Two uniform rods AB and BC have Young s modulii 1 2 x 10 1 N m and 1 5 x 10 1 N m respectively If coefficient of linear expansion of AB is 1 5 x 10 5 C and both have equal area of cross section then coefficient of linear expansion of BC for which there is no shift of the junction at all temperatures is 1 1 5x 10 51 C 3 0 6 x 10 5 C B 2 1 2 x 10 5 C 4 0 75 x 10 5 C

31 Three rods of same dimensions have thermal conductivities 3K 2K and K They are arranged as shown with their ends at 100 C 50 C and 0 C The temperature of their junction is 1 75 C 200 2 3 3 40 C 100 3K 100 C 2K K 50 C 0 C

8 Two conducting rods are joined in series as shown in the diagram Their conductivity are K and 2K Their length are in the ratio 2L and L respectively If extreme ends are maintained at 100 C and 0 C then the junction temperature T is Assume one dimensional steady state heat transfer T 100 C 1 80 C 3 40 C 2 L L 2 60 C 4 20 C 0 C

Two identical rods of silver and copper are coated with wax One end of each is put in a hot reservoir and other end is kept at room temperature Ratio of lengths upto which wax will melt is

The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel it is S If A is the linear coefficient of expansion of copper then the linear coefficient of expansion of silver is C S 3A b a c C S 3A 3 S 3A C 3 d 3 C S 3A 3

1 54 Three rods of equal length are joined to form an equilateral triangle PQR O is the mid point of PQ Distance OR remains same for small change in temperature Coefficient of linear expansion for PR and RQ is same i e a but that for PQ is a Then R APRF App X2 DEL A A2 2 ExPx Rx x1 4 42 2 Q P 042 a 3 g b a 4 a c a 3 d a 4

A steel tape measures the length of a copper rod as 90 0 cm when both are at 10 C the calibration temperature for the tape What would the tape read for the length of the rod when both are at 30 C Given a steel 1 2 x 10 5 per C and 1 7 x 10 5 per C acu 1 89 00 cm 2 90 21 cm 3 89 80 cm 4 90 01 cm

24 Density of a substance at 0 C is 10 6 gm c c and at 100 C is 10 gm c c coefficient of linear expansion of solid is 1 0 0006 C 3 0 0003 C 2 0 0004 C 4 0 0002 C

A planar lamina is made of thin unifor The length of section AB and EF is L and its coefficient is a The length of CD is L and its coefficient is a CB and DE are of same 01 3 5 Point s length having coefficient A B E and F reside on the same line that is sections AB and EF overlap Then find the for which the distance between end l A and end F remain same at all temperatures C ratio of A D F B F

x Two rods of material X sandwich another rod as shown in figure 1 19 At temperature T the three rods are in a state of zero strain and of length L and riveted to each other in this state If the temperature of the system increases to T AT find the final length of the system of the three rods Given that the coefficients of linear expansions of the rods and their Young s modulus for material X and Y are a a Y and Y respectively Consider a a rivets X

Consider two rods of same length and different specific heats S1 S conductivities K K and area of cross sections A1 A2 and both having temperature T and T2 at their ends If rate of loss of heat due to conduction is equal then A K A K242 C K A1 KA2 K 4 K 42 B S K2A1 K142 D S SF 2002

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

1x increase in Its temperature 0 ice when the ater of 2 Exercise 1 Fill in the blanks and rewrite the sentence The amount of water vapor in air is determined in terms of its humidity b If objects of equal masses are given equal heat their final temperature will be different This is due to difference in their Specific heat capacity c During transformation of liquid phase to solid phase the latent heat is latent a 2 Observe 1 kg Volume of water the following graph Considering the change in volume of water as its temperature is raised from 0 C discuss the difference in the behaviour of water and other substances What is this behaviour of water called 0 30 25 0 20 15 1 10 05 00 1 2 3 4 5 6 Temperature C 7 8 9 10 What is meant by specif C capacity How will you experimentally that substances have different heat capacities While deciding the unit fe which temperatures inte chosen Why Explain the following temp vs time graph Boiling water 100 90 80 70 60 50 40 30 20 10 A B 2 4 Water Liquid Liquid Ge 6 8 10 12 14 16 18 20 22 24 26 Time Minutes Ice Water Solid liquid 6 Explain the following La What is the role of ar behaviour of water in p aquatic life in regions climate b How can you relate the form water droplets on the oute of a bottle taken out of re with formation of dew LC In cold regions in winter crack due to anomolous of water

An ideal gas is expanding such that PT4 constant The coefficient of volume expansion of the gas is 1 11 T 2 3d T 15 3 T 4 4 T

9 It is desired to make a 20 2 coil of wire which has a zero thermal coefficient of resistance To do this a carbon resistor of resistance R is placed in series with an iron resistor of resistance R The proportions of iron and carbon are so chosen that R R 20 92 for all temperatures near 20 C Find the values of R and R 0 5 10 3 C airon 5 x 10 3 C 1 a carbon comperature with

obtained for an ideal gas from state A to B A P diagram is V The temperature of gas increases continuously The temperature of gas decreases continuously The temperature first increases then decreases The temperature first decreases then increases

It is seen that the potential energy can reach a maximum value of U at temperature T 10K Ifr and r are 0 9999 r and 1 0003 r for atoms of crystal A its approximate coefficient of linear expansion can be A 4 x 10 5 K B 1x 10 5 K C 2 10 K D 3 x 10 5 K 600

6 A horizontally oriented uniform copper roc of length is rotating about a vertical axis passing through its centre Calculate the rotated frequency at which the rod ruptures Breaking or rupture strength of copper is c and density of copper is p

16 A metal rod A of length expands by Al when its temperature is raised by 100 C Another rod B of different metal of length 2 expands by Al 2 for same rise in temperature A third rod C of length 36 is made up of pieces of rods A and B placed end to end expands by 24 on heating through 100 K The length of each portion of the composite rod is 5 4 1 3 0 3 0 3 3l 3l 2 2 2 l 2 4 2 3 7 zlo FH In the square f corners A an respectively o If A and C respectivley t

Estimate the speed of sound in air at standard temperature and pressure The mass of 7 1mole of air is 29 0 10 kg We know the Alitres at STP Therefore density of air at STP

30 C 200 7 2 mm 23 CRA CH Jo A a 0 000012 C

A faulty thermometer has its fixed points marked as 30 and 102 The temperature of body as measured by the faulty thermometer is 80 Find the correct temperature of t body on Celsius scale

A flask made of glass has a volume of 100 cm at 0 C What is its volume at 100 C Given coefficient of cubical expansion of glass is 2 5 X10 5 C Ans 100 25 cm

A piece of copper wire has a length of 2 m at 10 C Find its length at 100 C Coefficie of linear expansion of copper 17 x 10 C

A uniform disc is spinning about geometrical axis in free space Its temperature is increased by AT The fractional change in its angular velocity is a is coefficient of linear expansion 2 2 AT 4 aAT 1 2aAT 3 AT

A piece of steel has a length of 30 cm at 15 C At 90 C its length increases by 0 027 cm Find its coefficient of linear expansion

25 A diatomic ideal gas is heated at constant volume until its pressure is doubled It is again heated at constant pressure until its volume is doubled The molar heat capacity for the whole process is 1 2 23R 5 13R 4 2 4 19R 19R 6

A sphere of density p specific heat capacity c and radius r is hung by a thermally insulated thread in an enclosure which is kept constant at a lower temperature than the sphere The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of the sphere and is proportional to C 3 rp C 3r pc A B D 1 3 r pc 1 rpc

8 The square ABCD made of 4 metal rods AB BC CD and DA with point A and C remain fixed AB and AD have coefficient of linear expansion a and are heated by temperature t C BC and CD have coefficient of linear expansion a2 and are heated by t C tz t so that B and D move on perpendicular bisector of AC The temperature difference is proportional to SO

8 The length of a rod as measured in an experiment was found to be 2 48 m 2 46 m 2 49 m 2 50 m and 2 48 m Find the mean absolute error relative error and percentage error ns i 0 01m ii 0 004 m iii 0 4

by the gas heat absorbed by the gas A cylindrical tube of uniform cross sectional area A is fitted with two air tight frictionless pistons The pistons are connected to each other by a metallic wire Initially the pressure of the gas is P and temperature is To atmospheric pressure is also P Now the temperature of the gas is increased to 27 the tension in the wire will be A 2P A B PA wire C PA 2 D 4P A

constant A perfectly black body with an initial temperature of 573 K is allowed to cool in an evacuated constant temperature enclosure surrounded by melting ice at the rate of 0 346 C s Compute the Stefan s constant if mass of body is 24 gram specific heat of material of body is 0 1 cal gm C and area of body is 6 x 104 m 5 6 10 8 X

34 The rate of increase of thermo e m f with temperature at the neutral temperature of a AIPMT Prelims 2011 thermocouple 1 Is negative 2 Is positive 3 Is zero 4 Depends upon the choice of the two materials of the thermocouple

35 A Carnot engine whose sink is at 300 K has an efficiency of 40 By how much should the temperature of source be increased so as to increase its efficiency by 50 of original efficiency AIPMT Prelims 2006 1 275 K 2 325 K 3 250 K 4 380 K

The temperature coefficient of resistance of a wire is 0 00125 per degree celcius At 300 K its resistance is 1 ohm The resistance of the wire will be 2 ohms at a temperature 1 1154 K 3 600 K 2 1127 1127 K 4 1400 K

25 A bar is subjected to axial forces as shown If E is the modulus of elasticity of the bar and A is its area Its elongation will be cross section 3F 1 3 FI AE 3FI 2F 2 A 1 2FI AE 4FI F Fel 1 2 1938 3 Mg YA A Mg IA M

Question 18 A system of rods is assembled such that each rod has a length 1 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 Now answer the following questions A 2k k D k B k 2k C Temperature of junction D is Options a 1 4T b 1 6T c 1 8T

the above A cylindrical metal rod of length L and thickness d is shaped into a ring with a small gap x as shown On heating the system 1x1 a d 1 x decreases r and d increases 2 x and r increases d decreases 3 x r and d all increases 1 Data insufficient 100 C and 1 kg

wires of equal length are suspended as shown in figure Their Young s modulii are Y and Y respectively The equivalent Young s modulii will be 1 Y Y 3 Y Y C Y Y Y Y 4 Y Y 2

Steel rod at 40 C is observed to be 1 m long when measured by a brass scale which is correct at 0 C correct length of the steel rod at 0 C is steel 12x10 6 1 C and Brass 19 106 1 C 1 99 89 cm 3 99 97 cm 2 98 99 cm 4 89 6 cm

Click to see additional instructions 23 A particular sidewalk in a northern city is made up of a series of 1 5 meter long stone slabs whose coefficient of thermal expansion is 2 1x10 5 K 1 If the city s coldest winter temperatures are typically 22 C and its warmest summer temperatures are typically 34 C how much does each slab s length change as it undergoes these extremes Convert your final answer to millimeters