THERMAL EXPANSION OF MATERIALS

Size: px

Start display at page:

Download "THERMAL EXPANSION OF MATERIALS"

Buck Knight
6 years ago
Views:

1 HERMAL EXPANSION OF MAERIALS EXPANSION OF SOLIDS PREVIOUS EAMCE QUESIONS ENGINEERING. A cock penduum made of invar has a period of.5 sec, at C. If the cock is used in a cimate where the temperature averaes to C, how much time does the cock ose in each osciation? 7 (For invar, a 9 C, constant) (9 E) ).5 sec ).5 7 ) 5 7 sec 4).5 sec Ans : Loss or ain of time per day Δ t 86, , , 4 ime ose by the cock in each osciation ,4.5.5 S 86,4. One itre of oxyen at a pressure of atm and two itres of nitroen at a pressure of.5 atm. are introduced into a vesse of voume itre. If there is no chane in temperature, the fina pressure of the mixture of as (in atm) is (8 E) ).5 ).5 ) 4) 4 Ans : Resutant pressure PV + PV +.5 V + V. here is some chane in enth when a N tensie force is appied on a stee rod of area of cross-section - m. he chane of temperature required to produce the same eonation if the stee rod is heated, is (he moduus of Easticity is N/m and the coefficient of inear expansion of stee is ). (8 E) ) C ) 5 C ) C4) C Ans : herma force F ya Δt Δ t yaα. C 5 4. A penduum cock ives correct time at C at a pace where m/s. he penduum consists of a iht stee rod connected to a heavy ba. If it is taken to a different pace where. m/s, at what temperature the penduum ives correct time? (α of stee is 5 / C)

2 Ans : 4 ) C ) 6 C ) C 4) C ime period of simpe penduum L L π But L L ( + α ( t t) ) L + α ( t ) L. α ( t ) t C 5. wo ases A and B havin same pressure P, voume V and absoute temperature are mixed. If the mixture has the veocity and temperature as V and respectivey, then the pressure of the mixture is Ans : ) P ) P ) P/ 4) 4P [7 ] At constant temperature, Resutant pressure P PV + PV PV + PV R V+ V V P 6. he temperature of a thin uniform circuar disc, of one metre diameter is increased by C. he percentae increase in moment of inertia of the disc about an axis passin throuh its centre and perpendicuar to the circuar face (inear coefficient of expansion 6 / C) [6] Ans : ).55 ). ). 4).44 MR For circuar disc I Percentae increase in moment of inertia But R R ( + αt ) R R R I I I Squarin on both sides I ( + α ) ( ) I R t R I R

3 ( α ) R + t R R α t. 7. he reation between the coefficient of rea expansion ( γ r ) and coefficient of apparent expantion ( γ a ) of a iquid and the coefficient inear expantion ( α ) of the materia of the container is: [EAMCE 5] + ) γ α + γ ) γ α γ γ α + γ ) γ r α γα Ans: + + [ Since r α ] r r r r α r a a r α + 4) r ( α ) r α 8. he difference between voume and pressure coefficient of an idea as is : [5] ) /7 ) 7 ) /7 4) zero Ans : α β for any idea as α β 9. he type of a motor car contains air at 5 C. If the temperature increases to 5 C, the approximate percentae increase in pressure is (inore the expansion of tyre) (5 E) ) 7 ) 9 ) 4) Ans : As P from Chares aw P P P P P ΔP 7 P 98. A metaic soid sphere is rotatin about is diameter as axis of rotation. If the temperature is increased by C, the percentae increased in its moment of inertia is ( coefficient of inear expansion of the meta -5 / C ) [4 E] Ans : 4 I I Percentae increase in moment of inertia I Given I MR, I MR I I R R I R

4 But R R ( + t ) Squarin on both sides I ( ) I R + α t R I R t 5.4. he densities of a iquid at C and C are respectivey.7 and. A specific ravity botte is fied with m of the iquid at C up to the brim and it is heated to C. hen the mass of the iquid expeed in rams is [Coefficient of inear expansion of ass 9x - 6 / C] ( E). Ans:... d d d + rt r We know that [ ] d t t r r dt t r 5 / C.7 r r α 5 / C a r 98 / C mass of iquid exp eed ra mass of remainin iquid risein temp. On sovin we et r a A horizonta uniform ass tube of cm. enth seaed at both ends contains cm mercury coumn in the midde. he temperature and pressure of air on either side of mercury coumn are respectivey C and 76 cm of mercury. If the air coumn at one end is kept at C are the other end at 7 C, the pressure of air which is at C is (in cm of H) ( E) ) 76 ) 88. ).4 4) Ans: From as aw PV constant 9 x x x 6cm 9 6 cm 4

5 From idea as equation PV PV P P P P.4 cm of H. he coefficient of apparent expansion of a iquid when determined usin two different vesses A and B are γ and γ respectivey. If the coefficient of inear expansion of the vesse A is α, the coefficient of inear expansion of the vesse B is ( E ) αγ γ. γ+ γ γ γ α. γ γ + α. Ans: 4 γ r + rea app α γ + α γ + α α γ γ + α γ γ α + α γ γ he mass of oxyen as occupyin a voume of. it at a temperature 7 C and a pressure of 76mm of mercury in Kio rams is (moecuar weiht of oxyen ) ( E) + α Ans: PV nr P.4 R 7..() ( ) ( ) P. n R..() From () and ().4 7. n ( ) mass ( ).456 k 9 n m 5. A cosed hoow insuated cyinder is fied with as at C and aso contains an insuated piston of neiibe weiht and neiibe thickness at the midde point. he as at one side of the piston is heated to C.If the piston moves 5cm, the enth of the hoow cyinder is ( ) ).65cm ) 7.cm ) 8.6cm 4) 64.6 cm Ans:4 5

6 ( ) If the enth of the cyinder is then 64.6cm / 5 / When an air bubbe of radius r rises from the bottom to the surface of a ake, its radius becomes 5r / 4 ( the pressure of the atmosphere is equa to the m heiht of water coumn).if the temperature is constant and the surface tension is neected, the depth of the ake is () Ans: ).5m ) 6.5m ) 9.5m 4).5m Accordin to Boye s aw PV ( PV ) ( ) At thetopof theake Atthebottomof theake ( ) PV P + h V 4 5r 4 π [ + h] πr 4 6 h 9.5m A stee meter scae is to be rued so that miimeter intervas are accurate within about 5 X -5 mm at a certain temperature. he maximum temperature variation aowabe durin the ruin is (Coefficient of inear expansion of stee X -6 K - ) ( E) ) C ) 5 C ) 7 C 4) C Ans: So : We know α Δt ( ) 5 5 Δ α ( ) ( ) 5 C 8. When a iquid in a ass vesse is heated, its apparent expansion is.x -4 / C. Same iquid when heated in a metaic vesse, its apparent expansion is.6x -4 / C. he coefficient of inear expansion of meta is ( α ass 9x -6 / C) (EAMEC K, E). 5x -6 / C. 4x -6 / C. 5-6 / C 4. 7x -6 / C ( E) Ans:4 γapp + α γapp + α ass meta ( ) ( ) α 7 / C 9. A vesse is fied with an idea as at a pressure of atmospheres and temp. Haf of the mass of the as is removed from the vesse & the temp. of the remainin as is increased to. hen the pressure of the as in the vesse wi be )5 atm )6 atm ) 7 atm 4)8 atm ( E) Ans : 6

7 When haf the mass of the as is removed from the vesse, the pressure of the remainin as wi be 5 atm. P 5 atm P P K 6 k P? 6 P P 5 6 atm 7

8 MEDICAL. A cock penduum made of invar has a period of.5 sec, at C. If the cock is used in a cimate where the temperature a veraes to C, how much time does the cock ose in each osciation? 7 (For invar, a 9 C, constant) (9 M) ) Ans :.5 sec ) Loss or ain of time per day Δ t 86, , , 4 ime ose by the cock in each osciation ,4.5 86,4.5 7 ) 5 7 sec 4).5 sec.5 S. he voume of mercury in the bud of thermometer is -6 m. he area of cross-section of capiary tube is 7 sq.m. If the temperature is raised by C, the increase in the enth of the mercury 5 coumn is: ( γ 8 / ) H c (8 M) )8 cm ).9 cm )9 cm 4).8cm Ans : Voume -6 m, Area m 7, r 8 5 Δ t C V V [ + rδ t ] But voume Area enth 6 ( 7 ) m increase in enth m 9 cm. A two itre ass fask contains some mercury. It is found that at the temperature the voume of the air inside the fask remains the same. he voume of the mercury inside the fask is (α for ass 4 9 /, for mercury.8 / C ) (8 M) C γ Ans : 4 ) 5 c.c. ) 5 c.c. ) c.c 4) c.c. he condition for the voume of the air inside the fask remains the same at a temperatures is Vr Vr or Vr Vr 8

9 9.8 r cc.. 4 V. What fraction of the voume of a ass fask must be fied with mercury so that the voume of the empty space may be the same at a temperatures? (α ass 9 6 / C, γ H / C) [7 M] Ans : ) / ) /7 ) /4 4) /5 he condition for the voume of the air inside the fask remains the same at a temperatures is Vr V r V, V Voumes of iquid and ass V 8.9 V 9 V 5 7 V At a certain temperature, radius of an air bubbe is doubed when it comes to the top from the bottom of a mercury coumn of a heiht h. If the pressure at the [6 M] ) 5.5 ).64 ).45 4) 5. Ans : Accordin to the Boye s aw PV PV At the bottom PV ( P + hd ) V At the top PV PV o Where P is the atmospheric pressure 4 4 ( P + hd ) πr P πr + ( P hd ) r P( r ) On sovin h.64 m 5. he temperature of a as contained in a cosed vesse increases by C when the pressure is increased by %. he initia temperature of the as is [6 M] ) K ) K ) C 4) C Ans : Δp Δ From Chares aw p p 6. At a certain temperature, radius of an air bubbe is doubed when it comes to the top from the bottom of a mercury coumn of heiht h. If the pressure at the top is two atmospheres, the vaue of h in metres is 9

10 ) 5.5 ).64 ).45 4) 5. [5 E] Ans: + + r r r r α r a a r [ Since α ] 7. Equation of as in terms of pressure p absoute temperature and density d is. P d P d. P d P d. Pd Pd 4. Pd Pd (5 M ) Ans : From Idea as equation PVmR PV cons tan t P P d d 8. wo uniform meta rods of enths and and inear coefficients of expansion α and α respectivey are connected to form a sine rod of enth +. When the temperature of the combined rod is raised by tc o α, the enth of each rod increases by the same amount. hen α +α is (5 E) ) ) + ) 4) Ans: Increase in enth of the first rod increase in enth of the second rod Δ Δ ( iven) αδ t αδ t( iven) α α α α α α α + + α + α + α α α α + α +

11 9. At constant pressure, the ratio of increase in voume of an idea as per deree rise in Kevin temperature to its oriina voume is ( absoute temperature of the as) (4 M) ) ) ) / 4) / Ans: P constant V V + V + hen + V V V V V V. A thin brass sheet at C and thin stee sheet at C have the same surface area. he common temperature at which both woud have the same area (coefficient of inear expansion for brass and stee are respectivey 9 x -6 / C and x -6 / C) ( M).-.75 C C..75 C C Ans: S t S + β ( Δt) αbrass ( t ) αstee ( t ) 9( t ) ( t ) t.75 C. If pressure of an idea as contains in a cosed vesse is increased by.5% the increase in temperature is C the initia temperature of the as is ( M). 7 C. 7 C. C 4. 4 C Ans: P P at constant voume P.5 + P+ P 4K 7 C.5 +. wo marks on a ass rod, cm apart, are found to increase their distance by.8 mm, when the rod is heated from C to C. A fask made of the same ass as that of rod measures a voume c.c. at C. he voume, it measures at ºC in C.C is ( M) ).4 ) 4. ) 6.4 4) 8. Ans: ( ).8 ( ) ( )( ) We know α t t

12 8 / C Coefficient of voume expansion 4 / C γ α [ γ ] V V + t + ( 4 )( ).4 cc. A as is heated throuh C in a cosed vesse. Its pressure is increased by.4%. he initia temperature of the as is ( M). 5 C. C. -75 C 4. - C Ans: P P We know Let the initia pressure be K C 4. When the temperature of a body increases form t to t+ Δ t, its moment of inertia increases from I to I+ Δ. he coefficient of inear expansion of the body is. he ratio Δ I/I is : ( M) ) Δ t/t ) Δ t/t ) α Δ t 4) α Δ t Ans: 4 So : We know that the coefficient of superficia (or) aeria expansion A A ΔA β A Δt A Δt ( ) ( ) ΔA ΔA β β Δ A t A ( Δ ) ( t) ΔI ΔA But, α I A ΔI β( Δ t) ( α)( Δ t) I 5. If a cyinder of diameter.cm at C is to be sid into a hoe of diameter.9997 cm in a stee pate at the same temperature, the minimum required rise in the temperature of the pate is: (Coefficient of inear expansion of stee x -6 / C) ( M) ) 5 C ) 5 C ) 45 C 4) 55 C Ans:

13 Δ Δ We know α t t t ( Δ ) ( ) Δ t t α.9997 (.9997)( ) 6 herma Expansion of materias 6 5 C A specific ravity botte is fied upto the brim with mercury of 4, at C. When heated to 9 C, the mass of the mercury that over fows from the specific ravity botte is : (Coefficient of apparent expansion of mercury in ass is 65 / C) [ M] ) 5.46 ) 6.54 ).9 4).8 Ans : We know wt. of iquid expeed app wt. of remaininiquid riseintemp. γ ( )( ) x 65 ( 4 x)( 9) x 5.46m 7. wo meta rods A and B are havin their initia enths in the ratio : and coefficients of inear expansion in the ratio :4. When they are heated throuh the same temperature difference, the ratio of their inear expansion is ( M ) ) : ) : ) :4 4) 4: Ans: : : α: α :4 For the rod A ( α ) For the rob B ( α ) ( ) ( ) : : 4 : 8. he enth of a meta rod at C is.5m. When it is heated, its enth increases by.7mm. he fina temperature of rod is (coeff. of inear expansion of meta 9x -6 / C) [, M] Ans : 4 ) C ) C ) 4 C 4) 6 C We know the chane in temperature t (.7 ) (.5)( 9 ) t 6 5 ( ) As t C; t 6 C

ELASTICITY PREVIOUS EAMCET QUESTIONS ENGINEERING

ELASTICITY PREVIOUS EAMCET QUESTIONS ENGINEERING. If the ratio of engths, radii and young s modui of stee and brass wires shown in the figure are a, b and c respectivey, the ratio between the increase