topper’s package physics - xi kinetic theory & thermodynamics … · 2020-07-28 ·...

Topper’s Package Physics - XI Permutation and CombinationsKinetic Theory & Thermodynamics

117

1. GAS LAWS

1. The isochoric modulus of elasticity is

(a) zero (b) 1 (c) (d)

2. The temperature of an air bubble while risingfrom bottom to surface of a lake remainsconstant but its diameter is doubled. If thepressure on the surface is equal to h meter ofmercury column and relative density of mercuryis then the depth of lake is

(a) 2 h m (b) 4 h m

(c) 8 h m (d) 7 h m

3. If AB and CD are isotherms and AD and BC areadiabatic (figure) then the temperatures of

(a) B and C are same(b) A and C are same

A B

C D

V

P

(c) B and D are same

(d) Temperature of A is more than that of D

4. In the following diagram (Figure) the curvesbetween volume V and temperature T are drawnat two different pressures 1P and 2P . Whichpressure is less ?

(a) that associated with A(b) that associated with B V

T

A

B P1

P2

(c) both

(d) none of the above

5. A frictionless piston divides a gas cylinder intwo parts. g for the gas is 1.5. Initially theposition of the piston is such that the pressurein the first part is P and its volume is 4V andin the second part pressure is 8 P and volumeis 2V. Now the piston is released free. The finalpressure in the adiabatic process will be

(a) P (b) 2P (c) 22P (d) 4P

6. In the above problem, if the process isisothermal then the final pressure will be

(a)3

10 P (b)103 P (c)

713 P (d)

137 P

7. Liquid oxygen at 50 K is heated to 300 K atconstant pressure of 1 atm. The rate of heatingis constant. Which of the following graphsrepresent the variation of themperature withtime?

(a)

Temp

Time(b)

Temp

Time

(c)

Temp

Time(d)

Temp

Time

8. Two rigid boxes containing different ideal gasesare placed on a table. Box A contains one moleof nitrogen at temperature 0T , while Box Bcontains one mole of helium at temperature

073

T . The boxes are then put into thermalcontact with each other and heat flows betweenthem until the gases reach a common finaltemperature. (Ingore the heat capacity of boxes).Then, the final temperature of the gases, fT ,in terms of 0T , is

(a) 052fT T (b) 0

37fT T

(c) 073fT T (d) 0

32fT T

9. Temperature of an ideal gas is 300 K. Thechange in temperature of the gas when itsvolume chaanges from V to 2V in the processP = aV (Here a is positive constant) is

KINETIC THEORY &THERMODYNAMICS

Unit 10


118

(a) 900 K (b) 1200K(c) 600 K (d) 300 K

10. Figure shows two flasks connected to eachother. The volume of the flask 1 is twice thatof flask 2. The system is filled with an ideal gasat temperature 100 K and 200 K respectively.If the mass of the gas in 1 be m then what isthe mass of the gas in flask 2

(a) m (b) m/2(c) m/4 (c) m/8

11. Two non-reactive monoatomic ideal gases havetheir atomic masses in the ratio 2 : 3. Theratio f their partial pressure when enclosed ina vessel kept at a constant temperature is 4 :3. The ratio of their densities is(a) 1: 4 (b) 1 : 2(c) 6 : 9 (d) 8 : 9

12. A cylinder contains 10 kg of gas at pressure of107 N/m2. The quantity of gas taken out thecylinder, if final pressure is 2.5 106 N/m2,will be (Temperature of gas is constant)(a) 15.2 kg (b) 3.7 kg(c) zero (d) 7.5 kg

13. Inside a cylinder having insulating walls andclosed at ends is a movable piston, whichdivides the cylinder into two compartments. Onone side of the piston is a mass m of a gas andon the other side a mass 2m of the same gas.What fraction of volume of the cylinder will beoccupied by the larger mass of the gas whenthe piston is in equilibrium? Consider that themovable piston is conducting so that thetemperature is the same throughout?

(a) 14 (b) 1

3

(c) 12 (d) 2

3

14. The cylinder containing an ideal gas is invertical position and has a piston of mass M thatis able to move up or down without friction(figure.) If the temperature is increased

(a) Both p and V of the gas will change(b) Only p will increase according to Charles

law(c) V will change but not p(d) p will change but not V

15. Volume versus temperature graphs for a givenmass of an ideal gas is shown in figure. At twodifferent values of constant pressure. What canbe inferred about relation between p1 and p2

(a) p1 > p2 (b) p1 = p2(c) p1 < p2 (d) Data is sufficient

16. An inflated rubber balloon contains one mole ofan ideal gas, has a pressure p, volume V andtemperature T. If the temperature rises to 1.1T and the volume is increased to 1.05 V, thefinal pressure will be(a) 1.1 p (b) p(c) Less than p (d) Between p and 1.1p

17. Two thermally insulated vessles 1 and 2 are filledwith air at temperatures (T1, T2) volume (V1,V2) and pressure (P1, P2) respectively. If the valvejoining two vessels is opened, the temperatureinside the vessel at equilibrium will be

(a) T1 + T2 (b) (T1 + T2)/2

(c)

1 2 1 1 2 2

1 1 2 2 2 1

( )T T P V P VP V T P V T (d)

1 2 1 1 2 2

1 1 1 2 2 2

( )T T P V P VP V T P V T

18. The molecular weight of a gas is 44,. The volumeoccupied by 2.2 g of this gas at 0°C and 2 atm.pressure will be(a) 0.56 litre (b) 1.2 litres(c) 2.4 litres (d) 5.6 litres

19. Two vessels separately contain two ideal gasesto B at the same temperature the pressure of Abeing twice that of B. Under such conditions,


119

the density of is found to be 1.5 times the densityof B. The ratio of molecular weight of A and 6 is

(a) 34 (b) 2

(c) 12 (d) 2

320. Two identical glass bulbs are interconnected

by a thin glass tube A gas is filled in thesebulbs at N.T.P. If one bulb is placed in iceand another bulb is placed in hot bath, thenthe pressure of the gas becomes 1.5 times.The temperature of hot bath will be cylinderis

(a) 100°C (b) 182°C(c) 256°C (d) 546°C

21. Two spherical vessel of equal volume, areconnected by a narrow tube. The apparatuscontains an ideal gas at one atmosphere and300K. Now if one vessel is immersed in a bathof constant temperature 600K and the otherin a bath of constant temperature 300K. Thenthe common pressure will be

(a) 1 atm

(b) 45 atm

(c) 43 atm

(d) 34 atm

22. From the following P-T graph what inferencecan be drawn

(a) V2 > V1

(b) V2 < V1

(c) V2 = V1

(d) None of the above

23. PV versus T graph of equal masses of H2, Heand O2 is shown in fig. Choose the correctalternative

(a) C corresponds to H2, B to He and A to O2(b) A corresponds to He, B to H2 and C to O2(c) A corresponds to He, B to O2 and C to H2(d) A corresponds to O2, B to H2 and C to He

24. An ideal gas is initially at temperature T andvolume V. Its volume is increased by V dueto an increase in temperature T. pressureremaining constant. The quantity = V/(VT)varies with temperature as

(a) (b)

(c) (d)

25. The figure below shows the plot of PV/nTversus P for oxygen gas at two differenttemperatures.

Read the following statements concerning theabove curves:(i) The dotted line corresponds to the ‘ideal’

gas behaviour.(ii) T1 >T2(iii) The value of PV/nT at the point where

the curves meet on the y-axis is the samefor all gases.

Which of the above statement is true(a) (i) only (b) (i) and (ii) only(c) All of these (d) None of these


120

26. The change in volume V with respect to anincrease in pressure P has been shown inthe figure for a non-ideal gas at four differenttemperatures T1, T2, T3 and T4. The criticaltemperature of the gas is

(a) T1

(b) T2

(c) T3

(d) T4

27. n moles of an ideal gas undergoes a processA B as shown in the figure. The maximumtemperature of the gas during the process willbe

(a) 0 032P VnR (b) 0 09

2P VnR

(c) 0 09P VnR (d) 0 09

4P VnR

2. SPEED OF A GAS

28. Three closed vessels A, B and C are at thesame temperature and contain gases whichobey the Maxwellian distribution of velocities.Vessel A contains only O2, B only N2 and Ca mixture of equal quantities of O2 and N2.If the average speed of O2 molecules in vesselA is v1, that of N2 molecules in vessel B isv2, then the average speed of O2 moleculesin vessel C is (M is the mass of oxygenmolecule)

(a) 1 2v v2

(b) 1v

(c) 1 2v v (d) B3k T2

29. The average translational energy and the rmsspeed of molecules in a sample of oxygen gas at300 K are 6.21 10–21 J and 484 ms–1

respectively. The corresponding values at 600 Kare nearly (assuming ideal gas behaviour)

(a) 21 112.42 10 J, 968 ms (b) 21 18.78 10 J, 684 ms (c) 21 16.21 10 J, 968 ms (d) 21 112.42 10 J, 684 ms

30. Cooking gas containers are kept in a lorrymoving with uniform speed. The temperatureof the gas molecules inside will(a) Increase(b) Decrease(c) Remain same(d) Decrease for some, while increase for

others31. If the molecular weight of two gases are M1 and

M2, then at a temperature the ratio of root meansquare velocity v1 and v2 will be

(a)1

2

MM (b)

2

1

MM

(c)1 2

1 2

M MM M

(d)

1 2

1 2

M MM M

32. At which temperature the velocity of O2molecules will be equal to the velocity of N2molecules at 0°C(a) 40°C(b) 93°C(c) 39°C(d) Cannot be calculated

33. Three closed vessels A, B and C are at the sametemperature T and contain gases which obeythe Maxwellian distribution of velocities. VesselA contains only O2, B only N2 and C a mixture ofequal quantities of O2 and N2. If the averagespeed of the O2 molecules in vessel A is V1 thatof the N2 molecules in vessel B is V2, theaverage speed of the O2 molecules in vessel Cis

(a) (V1 + V2)/2 (b) V1

(c) (V1V2)1/2 (d) 3kT /M

34. The curve between absolute temperature and2rmsv is

(a) (b)


121

(c) (d)

35. The mean free path of molecules of a gas, (radiusr) if inversely proportional to(a) r (b) r(c) r3 (d) r2

36. At what temperature will the rms speed ofoxygen molecules become just sufficient forescaping from the Earths atmosphere Given :Mass of oxygen molecule (m) = 2.76 10–26 kgBoltzmann’s constant kB = 1.38 10–23 JK–1)(a) 2.508 104 K (b) 8.360 104 K(c) 5.016 104 K (d) 1.254 104 K

3. DEGREE OF FREEDOM & SPECIFIC HEAT

37. n1 and n2 mols of two ideal gases ofthermodynamic constant 1 and 2 respectively

are mixed. p

v

CC for the mixture is

(a) 1 22

(b)1 1 2 2

1 2

n nn n

(c)1 2 2 1

1 2

n nn n

(d)1 1 2 2 2 1

1 2 2 1

( 1) ( 1)( 1) ( 1)

n nn n

38. Equal volumes of monoatomic and diatomicgases of same initial temperature and pressureare mixed. The ratio of the specific heats of themixture ( / )p vC C will be(a) 1 (b) 1.5(c) 1.52 (d) 1.53

39. 1n mole of monoatomic gas is mixed with 2nmole of diatomic gas such that mixture 1.5 (a) 1 2n 2n (b) 2 1n 2n(c) 1 2n n (d) 1 2n 3n

40. The ratio of the adiabatic Bulk modulus to theisothermal Bulk modulus of a perfect gas with fdegrees of freedom is

(a)2f (b)

11f

(c) 21f

(d)( 1)1

3

f

41. A vessel contains a mixture of one mole ofoxygen and two moles of nitrogen at 300 K. Theratio of the average rotational kinetic energyper oxygen molecule to per nitrogen molecule is(a) 1 : 1 (b) 1 : 2(c) 2 : 1(d) Depends on the moment of inertia of the

two molecules

42. If pC and vC denote the specific heats ofnitrogen per unit mass at constant pressure andconstant volume respectively, then

(a) 28p vC C R (b)28p vRC C

(c)14p vRC C (d) p vC C R

43. Internal energy of n1 moles of hydrogen attemperature T is equal to the internal energy ofn2 moles of helium at temperature 2 T. Thenthe ratio n1/n2 is(a) 3/5 (b) 2/3(c) 6/5 (d) 3/7

44. The number of translational degrees of freedomfor a diatomic gas is(a) 2 (b) 3(c) 5 (d) 6

45. One mole an ideal diatomic gas undergoes atransition from A to B along a path AB as shownin the figure,The change in internal energy ofthe gas during the transition is

(a) –20kJ (b) 20J(c) –12kJ (d) 20kJ

46. An ideal gas with heat capacity at constantvolume CV undergoes a quasistatic processdescribed by PV in a P - V diagram, where is a constant. The heat capacity of the gasduring this process is given by(a) CV (b) CV + nR

(c) VnRC

1

(d) V 2nRC

1

47. The specific heat of an ideal gas is


122

(a) Proportional to T (b) Proportional to T2

(c) Proportional to T3 (d) Independent of T

48. The amount of heat energy required to raisethe temperature of 1 g of Helium at NTP, fromT1K to T2K is

(a)2

a B1

T3 N k4 T

(b) a B 2 13 N k T T8

(c) a B 2 13 N k T T2

(d) a B 2 13 N k T T4

49. The molar specific heats of an ideal gas atconstant pressure and volume are denoted by

Cp and Cv, respectively. If p

v

CC

and R is theuniversal gas constant, then Cv is equal to

(a) R (b)11

(c)R

( 1) (d)( 1)

R

50. Cp and Cv are specific heats at constantpressure and volume respectively. It is observedthat Cp – Cv= a for hydrogen gas, Cp – Cv= b fornitrogen gas(a) a = 28b (b) 1a b

14

(c) a = b (d) a = 14b

51. One mole of an ideal monatomic gas undergoesa process described by the equation PV3 =constant. The heat capacity of the gas duringthis process is

(a) R (b) 3 R2

(c) 5 R2 (d) 2R

52. When an ideal monoatomic gas is heated atconstant pressure, fraction of heat energysupplied which increases the internal energyof gas, is(a) 2/5 (b) 3/5(c) 3/7 (d) 3/4

53. A gaseous mixture consists of 16g of helium and

16g of oxygen. The ratio P

V

CC of the mixture is

(a) 1.4 (b) 1.54(c) 1.59 (d) 1.62

54. An ideal diatomic gas is heated at constantpressure. The the ratio of the work done to theheat supplied is

(a) 35 (b) 2

5

(c) 27 (d) 4

755. One mole of Ideal monoatomic gas ( = 5/3) Is

mixed with one mole of diatomic gas ( = 7/5).What is for the mixture? denotes the ratio ofspecific heat at constant pressure, to that atconstant volume(a) 3/2 (b) 23/15(c) 35/23 (d) 4/3

56. An ideal gas undergoes a quasi static, reversibleprocess in which its molar heat capacity Cremains constant. If during this process therelation of pressure P and volume V is given byPVn = constant, then n is given by (Here CP andCV are molar specific heat at constant pressureand constant volume, respectively)

(a) P

V

C Cn

C C

(b) P

V

C Cn

C C

(c) V

P

C Cn

C C

(d) P

V

Cn

C

4. PRESSURE & ENERGY

57. The pressure and density of a diatomic gas( 7/5) changes from ( )P to ( )P during

adiabatic change. If 32

then

PP will be

(a) 128 (b) 1/128(c) 32 (d) 1/32

58. 1 mole of an ideal gas is contained in a cubicalvolume V, ABCDEFGH at 30OK (figure). Oneface of the cube (EFGH) is made up of amaterial which totally absorbs any gasmolecule incident on it. At any given time,

(a) The pressure on EFGH would be zero(b) The pressure on all the faces will the equal(c) The pressure of EFGH would be double the

pressure on ABCD(d) The pressure of EFGH would be half that

on ABCD59. The pressure is exerted by the gas on the walls


123

of the container because(a) it loses kinetic energy(b) it sticks with the walls(c) On collision with the walls there is a

change in momentmum(d) it is accelerated towards the walls

60. A cubic vessel (with face horizontal + vertical)contains, an ideal gas at NTP. The vessel isbeing carried by a rocket which is moving ata speed of 500 ms–1 in vertical direction. Thepressure of the gas inside the vessel asobserved by us on the ground(a) Remains the same because 500 ms–1 is

very much smaller than vrms of the gas(b) Remains the same because motion of the

vessel as a whole does not affect therelative motion of the gas molecules andthe walls

(c) Will increase by a factor equal to2 2 2rms rms(v (500) )/ v where vrms was the

original mean square velocity of the gas(d) Will be different on the top wall and bottom

wall of the vessel61. 1 mole of H2 gas is contained in a box of

volume V = 1.00 m3 at T = 300 K. The gas isheated to a temperature of T = 3000 K and thegas gets converted to a gas of hydrogen atoms.The final pressure would be (considering allgases to be ideal)(a) Same as the pressure initially(b) 2 times the pressure initially(c) 10 times the pressure initially(d) 20 times the pressure initially

62. A horizontal uniform glass tube of 100 cm,length sealed at both ends contain 10 cmmercury column in the middle. Thetemperature and pressure of air on either sideof mercury column are respectively 31°C and76 cm of mercury. If the air column at oneend is kept at 0°C and the other end at 273°C,the pressure of air which is at 0°C is (in cmof Hg)(a) 76 (b) 68.2(c) 102.4 (d) 122

63. One kg of a diatomic gas is at a pressure of8 104 N/m2.The density of the gas is 4 kg/m3. What is the energy of the gas due to itsthermal motion(a) 3 104J (b) 5 104J(c) 6 104 J (d) 7 l04 J

64. Three perfect gases at absolute temperatureT1, T2 and T3 are mixed. The masses ofmolecules are m1, m2 and m3 and the numberof molecules are n1, n2 and n3 respectively.Assuming no loss of energy, the finaltemperature of the mixture is

(a) 1 2 3(T T T )3

(b)

1 1 2 2 3 3

1 2 3

n T n T n Tn n n

(c)2 2 2

1 1 2 2 3 3

1 1 2 2 3 3

n T n T n Tn T n T n T

(d)

2 2 2 2 2 21 1 2 2 3 3

1 1 2 2 3 3

n T n T n Tn T n T n T

65. The graph which represents the variation ofmean kinetic energy of molecules withtemperature t°C is

(a) (b)

(c) (d)

66. The volume (V) of a monatomic gas varies withits temperature (T), as shown in the graph. Theratio of work done by the gas, to the heatabsorbed by it, when it undergoes a changefrom state A to state B, is

(a) 25

(b) 23

A

BV

T

(c) 13

(d) 27

5. LAWS OF THERMODYNAMICS AND PROCESS

67. Initial and final pressures and volumes of a gasare P1, V1 and P2, V2 respectively. If PVn =constant then the amount of work done will be(a) minimum for n

(b) minimum for 1n

(c) maximum for 1n


124

(d) maximum for 0n

68. The adiabatic bulk modulus of elasticity forhydrogen gas at NTP is(a) 5 210 /N m (b) 8 210 /N m(c) 8 21.4 /N m (d) 5 21.4 10 /N m

69. In a thermodynamic process, the pressure of acertain mass of gas is changed in such a waythat 20 Joule heat is released from it and 8 Joulework is done on the gas. If the initial internalenergy of the system is 30 Joule then the finalinternal energy will be(a) 42 Joule (b) 2 Joule(c) 18 Joule (d) 58 Joule

70. Air is filled in a motor car tube at 27°Ctemperature and 2 atmosphere pressure. If thetube suddenly bursts, then the final temperature

will be 12

0 822 7F

HGIKJ

RS|T|

UV|W|

/

.

(a) 246.0 K (b) 642 K(c) 300 K (d) 563 K

71. The amount of heat necessary to raise thetemperature of 0.2 mol of 2N at constantpressure from 37° to 337°C will be(a) 1764 Joule (b) 764 Joule(c) 1764 Calorie (d) 1764 erg

72. The minimum number of thermodynamicparameters required to specify the state of a gassystem is(a) two (b) one(c) three (d) infinite

73. In the following diagrams, the variations ofvolume units pressure are shown. A gas istaken via path ABCDA. The change in internalenergy will be

(A)

D C

B A

V

P (B)

D C

B A

V

P

(C)

D C

B A

V

P (D)

D C

B A

V

P

(a) positive in all from A to D(b) positive in A, B and C but zero in D(c) negative in A, B and C but zero in D

(d) zero from A to D in all

74. An ideal gas is taken via paths AB, BC and CAas shown in figure. The net work done in thewhole cycle is

(a) 1 13P VC

B A

V

P

P1

4P1

3V1 V1

(b) 1 13P V

(c) 1 16P V

(d) 1 112P V

75. The relation between the internal energy U andadiabatic constant is

(a)PVU

1 (b)

PVU1

(c)PVU

(d) PVU

76. A gas has a molar specific heat vC at constantvolume. n moles of this gas is heated such thatrise in temperature is T. The internal energychanges by an amount nCv T(a) only if T occurs at constant pressure(b) only T occurs at constant volume(c) in any non-adiabatic process(d) in any known process

77. A mono-atomic gas expands at constant pressureon heating. The percentage of heat supplied thatincreases the internal energy of the gas and thatis involved in the expansion is(a) 75 %, 25 % (b) 25 %, 75 %(c) 60 %, 40 % (d) 40 % 60 %

78. One mole of an ideal gas with heat capacity pCat constant pressure undergoes the process

0T T V where 0T and are constants. Ifits volume changes from 1V to 2V , the amountof heat transferred to the gas is

(a) 2p 0

1

VC RT ln

V

(b) 2 1 2p

0 1

(V V ) VC ln

RT V

(c) 2p 2 1 0

1

VC (V V ) RT ln

V

(d) 20 p 1 2

1

VRT ln C (V V )

V


125

79. A cyclic process is shown on the V-T diagram.The same process on a P-T diagram is shown by

T

V

AB

C

O

D

(a)

T

P

A B

CO

D(b)

T

PA

BCO

D

(c)

T

P

A

BC

O

D (d)

T

P

AB

C

O

D

80. An ideal gas is taken through A B C A, as shown in figure. If the net heat supplied tothe gas in the cycle is 5 J, the work done by thegas in the process C A is

A

BC2

1V(m

)3

P(N/m )2101

(a) – 5 J (b) – 10 J(c) – 15 J (d) – 20 J

81. When a system is taken from state i to state falong the path i a f, it is found that Q = 50 Caland W = 20 Cal . Along the path i b f Q = 36 CalW along the i b f is

(a) 14 Cal a f

i b

(b) 6 Cal

(c) 16 Cal

(d) 66 Cal

82. Heat is supplied to a diatomic gas at constantpressure. The ratio of : :Q U W is

(a) 5 : 3 : 2 (b) 5 : 2 : 3(c) 7 : 5 : 2 (d) 7 : 2 : 5

83. An ideal monoatomic gas is taken around thecycle ABCDA as shown in the p-V diagram. Thework done during the cycle is

(a) pV

(b) 2 pV

(p,V)

(2p,V) (2p,2V)

(p,2V)

p

V

B C

A D(c)12

pV

(d) zero

84. The ratio of work done by an ideal monoatomicgas to the heat supplied to it in an isobaricprocess is

(a)25 (b)

32

(c)35 (d)

23

6. HEAT ENGINE & SECOND LAW OF THERMO.

85. A Carnot engine has same efficiency between(i) 100 K and 500 K and (ii) T K and 900 K. Thevalue of T is(a) 90 K (b) 180 K(c) 270 K (d) 360 K

86. A Carnot engine takes 310 kilocalories of heatfrom a reservoir at 627°C and exhausts it to asink at 27°C. The efficiency of the engine willbe(a) 22.2% (b) 33.3%(c) 44.4% (d) 66.6 %

87. In the above problem, the work performed bythe engine will be(a) 61.4 10 Joule (b) 62.8 10 Joule(c) 64.2 10 Joule (d) 65.6 10 Joule

88. A reversible engine takes heat from a reservoirat 527°C and gives out to the sink at 127°C.The engine is required to perform usefulmechanical work at the rate of 750 watt. Theefficiency of the engine is(a) 10 % (b) 30 %(c) 50 % (d) 70 %

89. Two Carnot engines A and B are operated insuccession. The first one, A receives heat froma source at T1 = 800 K and rejects to a sink atT2K. The second engine B receives heatrejected by the first engine and rejects toanother sink at T3 = 300 K. If the work outputsof two engines are equal, then the value of T2 is


126

(a) 100 K (b) 300 K(c) 490 K (d) 700 K

90. A Carnot’s engine having an efficiency of = 1/10 as heat engine, is used as arefrigerator. If the work done on the system is10 J, the amount of energy absorbed from thereservoir at lower temperature is(a) 100 J (b) 99 J(c) 90 J (d) 1 J

7. INTEGER TYPE QUESTIONS

1. A cylinder of cross-section area A has two pistonsof negligible mass separated by distances l loadedwith spring of negligible mass. An ideal gas attemperature T1 is in the cylinder where thesprings are relaxed. When the gas is heated bysome means its temperature becomes T2 andthe springs get compressed by l/2 each. If P0 isatmospheric pressure and spring constant k =

02P Al , then find the ratio of T2 and T1.

2. A vessel contains 1 mole of O2 (molar mass 32)at a temperature T. The pressure of the gas isP. An indentical vessel containing one mole ofHe gas (molar mass 4) at a temperature 2T hasa pressure of xP. Find the value of x.

3. One mole of a gas is taken from state A to stateB as shown in figure. Work done by the gas is

10 J. Find the value of . [Given: T1 = 320

K, R = 353 ]

4. The relation between internal energy U,pressure P and volume V of a gas in an adiabaticprocess is : U = a + bPV where a = b = 3.Calculate the greatest integer of the ratio ofspecific heats [ ].

5. One mole of an ideal monatomic gas undergoesthe process P = 1/2T , where is costant. Ifmolar heat capacity of the gas is R when R= gas constant then find the value of .

6. One mole of a monoatomic gas is enclosed ina cylinder and occupies a volume of 4 liter ata pressure 100 N/m². It is subjected to a processT = V², where is a positive constant, V isvolume of the gas and T is Kelvin temperature.Find the work-done by gas (in joule) inincreasing the volume of gas to six times initialvolume

7. The value of = CP/CV is 4j/3 for an adiabaticprocess of an ideal gas for which internalenergy U = K + nPV. Find the value of n (K isconstant)

8. One mole of a monoatomic ideal gas follows aprocess AB, as shown. The specific heat of the

process is 13R

6 . Find the value of n on P-axis.

10. Heat Q =32 RT is supplied to 4 moles of an ideal

diatomic gas at temperature T, which remainsconstant. How many moles of the gas aredissolved into atoms?


127

1. GAS LAWS1. c 2. d 3. d 4. b 5. c6. b 7. d 8. d 9. a 10. c11. d 12. d 13. d 14 c 15. a16. d 17. c 18. a 19. a 20. d21. c 22. a 23. a 24. c 25. c26. b 27. d

2. SPEED OF A GAS28. b 29. d 30. c 31. b 32. c33. d 34. c 35. d 36. b

3. DEGREE OF FREEDOM AND SPECIFIC HEAT37. d 38. b 39. c 40. c 41. a42. b 43. c 44. b 45. a 46. c47. a 48. b 49. c 50. d 51. a52. b 53. d 54. c 55. a 56. a

4. PRESSURE AND ENERGY57. a 58. d 59. c 60. b 61. d62. c 63. b 64. b 65. c 66. a

5. LAWS OF THERMODYNAMICS AND PROCESS67. a 68. d 69. c 70. a 71. a72. a 73. d 74. b 75. a 76. d77. c 78. c 79. a 80. a 81. b82. c 83. a 84. a

6. HEAT ENGINE AND SECOND LAW OF THERMODYNAMICS85. b 86. d 87. b 88. c 89. c90. c

7. HEAT ENGINE AND SECOND LAW OF THERMODYNAMICS1. (4) 2. (2) 3. (7) 4. (1)5. (2) 6. (7) 7. (3) 8. (6) 9. (3)

topper’s package physics - xi kinetic theory & thermodynamics … · 2020-07-28 ·...

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