Kinetic Theory of Gases

Kinetic Theory of Gases9

COMPREHENSIVE REVIEW

1. Ideal gas or Perfect gas

i) The molecules of the ideal gas are point

masses, with zero volume.

ii) There is no intermolecular force for the

molecules of ideal gas.

iii) There is no intermolecular potential energy

for the molecules of ideal gas.

iv) The molecules of ideal gas possess only the

kinetic energy.

v) Change in internal energy of one mole of

ideal gas is : U = CT.

vi) The ideal gases strictly obey the gas

equation, Boyle's law, Charle's law etc. at

all temperatures and pressures.

vii) The coefficient of cubical expansion of ideal

gas is equal to 1

273 per kelvin.

viii) The coefficient of pressure vanation with

temperature for ideal gas is equal to 1

273

per kelvin.

ix) The specific heat of ideal gases does not

depend on temperature.

x) No gas in the universe is ideal. Gases

such as H2, N

2, O

2, etc. behave very similar

to ideal gases.

xi) Monoatomic inert gases also behave like

ideal gases.

xii) The behaviour of real gases at high tempe-

rature and low pressure is very similar to

the ideal gases.

2. Ideal gas equation

For n moles of ideal gas, the relation between

pressure (P), volume (V) and the temperature

(T), is :

pV nRT

It is called ideal gas equation.

KINETIC THEORY OF GASES ( 202 )

i) For one mole, the ideal gas equation is :

pV RT

Here R is called molar gas constant. Its

value is same for all gases.

ii) For one gram of gas, we have

pV rT

Here r is specific gas constant.

Rr ,

M where M is molecular weight of the

gas.

iii) The value of r is different for different

gases.

iv) Values of R

R 8.4 J/moI K

R 2 cal/mol K

v) Dimensional formula for R is,

ML2T–2 –1 mol–1

3. Avogadro's hypothesis

i) Equal volumes of all gases at the same

temperature and pressure contain the same

number of molecules.

ii) One mole of every gas at NTP has same

volume equal to 22.4 litres.

iii) One mole of every gas contains same

number of molecules called Avogadro's

numbers NA = 6.02 1023.

iv) Avogadro's number is also equal to the

number of atoms in 12 g of carbon-12 atom.

4. Real gases

i) The gases actually found in nature are called

real gases.

ii) The molecules of the real gas have finite

volume.

iii) There is intermolecular attraction or repulsion

between the molecules of the real gas.

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iv) The intermolecular force is attractive at

larger intermolecular separation and

repulsive, when the molecules are too close

to each other.

v) The molecules of the real gas have inter-

molecular potential energy as well as kinetic

energy.

vi) Real gases can be liquified as well as

solidified.

5. NTP or STP

i) NTP stands for normal temperature and

pressure.

ii) STP stands for standard temperature and

pressure.

iii) NTP refers to a temperature of 250C and

1 atm pressure. STP refers to a temperature

of 273 K or 00C and 1 bar pressure (slightly

lesser than 1 atm pressure).

iv) 1 atm. pressure = 76 cm of Hg pressure

1.01 105 Pa

1 bar = 105 Pa = 0.987 atm. pressure

6. Absolute zero

i) The absolute zero refers to zero of the kelvin

scale. That is absolute zero = 0 K = –2730C.

Exact value of absolute zero is –273.150C.

ii) At the absolute zero all molecular motion

ceases.

iii) The volume of ideal gas becomes zero at

the absolute zero.

iv) The pressure of ideal gas becomes zero at

the absolute zero.

v) The molecular energy or internal energy of

the ideal gas becomes zero at the absolute

zero.

vi) All real gas get liquified before reaching the

absolute zero.

vii) The internal energy of the real gases (after

liquifaction) at the absolute zero is not zero.

It is called zero point energy or Fermi

energy.

7. Postulates of the kinetic theory of gases

i) Nature of molecules

a) The molecules of each gas are identical

but different from that of other gases.

b) Molecules of a gas are point masses.

c) Molecules are rigid & perfectly elastic

spheres.

ii) Motion of molecules

Molecules of the gases move randomly in

all directions with all possible velocities.

iii) Collisions

a) The molecules of the gas continuously

collide with one another as well as with

the walls of the containing vessels.

b) The molecular collisions are perfectly

elastic.

c) The total energy of the molecules

remains constant during collisions.

d) Molecules move with constant velocity

along a straight line during the two

collisions.

e) The time spent in a collisions (10–8 s)

is very very small as compared to that

between the two collisions.

f) The number of collisions per second

does not change with time, provided

physical conditions such as pressure

and temperature do not change.

g) Collisions cause no change in the

density of the gas in any part of the

sample.

iv) Intermolecular forces

a) There is no intermolecular force

(perfect gas).

b) Gravitational attraction between the

molecules is negligible and so it is not

taken into account.

v) Pressure

a) Continuous collisions of the molecules

with the walls of the containing vessel

cause pressure on the walls.

b) Continuous collisions of the molecules

also cause pressure at all points within

the gas.

8. Expression for the pressure of gas

The expression for the pressure of the perfect

gas is :

2

rms

1p C

3

where, = density of the gas and Crms

is the root

mean square speed of the molecules.





Other expressions for pressure of the gas

Suppose, M is the mass of the gas and V is the

volume of the gas. Then,

M

V

Hence2

rms

1 Mp C

3 V

i) If the number of molecules in the gas sample

be N and mass of each molecule be m, then :

p =

2

rmsNmC1

3 V

= 2

rms

2 1 1N mC

3 V 2

= 2 1

E3 V

[Here E is total kinetic energy of all the

molecules]

That is p Average kinetic energy of all

the molecules.

ii) From the above expressions we conclude

that :

(i) 2p C (ii) p KE

(iii) p p (iv) p M

(v) p m (vi)1

pV

where the symbols have their usual meanings.

9. Kinetic interpretation of energy

The expression for pressure of a gas is :

2 2

rms rms

1 1 Mp C C

3 3 V

If M is the mass of one mole and V be the volume

of one mole then : from the gas equation, we find :

pV RT

Here2

rms

1pV RT MC

3

Or2

rms

1 MT C

3 R

Or 2

rmsT C

That is, the temperature of the gas is directly

proportional to the square of the rms velocity of

the gas molecules.

i) In other words, if C1 rms

& C2 rms

be the rms

speeds at temperatures T1 & T

2 respectively,

then :

2

1 rms1

2

2 2 rms

CT

T C

Or1 rms 1

2 rms 2

C T

C T

This is called kinetic interpretation of

temperature.

ii) Root mean square velocity for one

molecule

For one mole of gas, we have

2

rms

1pV RT MC

3

Or rms

3RTC

M

If NA be the Avogadro's numbers, then

R = NAk, where k is Boltzmann constant.

And M = NAm, where m = mass of a

molecule.

Hence Arms

A

3N kTC

N m

Orrms

3kTC

m

iii) For two gases of molecular weights M1 and

M2 at temperatures T

1 and T

2, we find :

1 rms 2 1

2 rms 1 2

C M T

C M T

iv) At absolute zero, we have T = 0. Hence

Crms

= 0. That is, the root mean square speed

of all molecules at absolute zero is zero.

That is, at absolute zero, all molecular

motion ceases.

v) Since 2

rmsT C and 2

rmsC cannot be –VE.

Hence, the absolute temperature or kelvin

temperature can never be –VE.





vi) Root mean square velocity of the molecules

of a gas depends on the temperature alone.

vii) Root mean square velocity of the molecules

of a gas does not depend on the volume or

pressure of the gas, because :

a) When pressure changes at constant

temperature p

= constant.

b) When volume changes at constant

temperature. p V = constant. Hence

rms

2p 3pVC constant

M

viii) If C be the speed of sound in the gas, then

pC

where p

C

C

= the ratio of molar specific

heats at constant volume and constant

pressure respectively.

Also rms

3pC

Hence rms

3C C

10. Other general characteristics of the gas, in

connection with the kinetic theory of gases

i) The size of the molecules is negligible as

compared to the average intermolecular

separation, which is of the order of 10–9 m.

ii) The volume of the molecules is negligible

as compared to the volume of the gas

sample. For one mole of a gas at NTP, the

volume of all the molecules added together

may be around 0.014% of the volume of

the gas as a whole.

iii) The time of collision of the molecules is of

the order of 10–8 s. The time elapsed

between two collisions is very very large as

compared to the time of collisions.

iv) In actual gases or real gases, there is

intermolecular force. It is attractive when

the molecules are far apart and it is repulsive

when the molecules are too close to each

other.

v) Continuous collisions of the molecules with

the walls cause pressure of the gas.

11. Average kinetic energy of the molecules

The average kinetic energy of one mole of ideal

gas is :

k

3U RT

2

The mean kinetic energy of the molecule of an

ideal gas is :

k (molecule)

3U kT

2

where, k = Boltzmann's constant.

The above relations are not true for the real gases,

in which case the energy depends on the number

of atoms in each molecule of the gas. The above

relations are true for monoatomic real gases.

12. pV-graphs at constant temperature





13. V-T graph at constant pressure

14. p-T graph at constant volume

15. Other graphs

i) Kinetic energy – Temperature graph

ii)rmsC T graph

iii)rmsC T graph

16. Gas Laws

i) Boyle's law

At constant temperature the pressure (p)

of the gas is inversely proportional to the

volume (V) of the gas. That is :

1p

V

or pV = constant

ii) Charle's law

At constant pressure, the volume (V) of the

gas is directly proportional to the absolute

temperature (T). That is :





V T

OrV

T = constant

iii) Gay Lussac's law

At constant volume, the pressure (p) of the

gas is directly proportional to the temperature.

That is :

p T

Orp

constantT

17. Specific heat

It is the amount of heat required to raise the

temperature of unit mass of a substance through

one degree. Its dimensional formula is, 2 1 1L T .

It may be expressed in cal/g0C, kcal/kg0C,

BTU/1b0F, J/kg K.

*cal/g0C = kcal/kg0C

4.2 103 J/kg K

We know that,

Q ms T or Q

sm T

where, Q = amount of heat required

m = mass of the substance

s = specific heat of the substance

Specific heat of real gases varies directly with

temperature. That is,

VC T

i) Internal energy of real gas depends on

volume as well as temperature.

ii) The change in internal energy of one mole

of real gas is given by :

V 2

aU C T V

V

iii) The real gases do not obey the Joule's law.

That is,

V

U0

V

Solids and liquids have only one specific heat.

Because on increasing the temperature of solids

and liquids, the change in volume is very small.

On the other hand, gases have two specific

heats. Because in this case, on increasing the

temperature of a gas, increase in volume is large.

Specific heat at constant volume (CV)

Here, the volume is constant. So, no external

work is done. In this case, only internal energy

rises.

Specific heat at constant pressure (CP)

Here, the pressure is constant and there is

increase in the volume. The energy is absorbed

to do the external work against external pressure.

CP is always greater than C

V.

18. Molar specific heat

The amount of heat required to raise the

temperature of 1 mole of substance through 1 K

is called molar specific heat. It is denoted by C.

Its unit is J/mol K. It is generaly used for gases.

* For the gases, molar specific heat is

defmed at constant volume (CV) and at constant

pressure (CP). It is found that C

P – C

V = R, where

R is molar gas constant.

Also, R = 8300 joule/mole/degree

19. Latent heat

Heat required to change the state (from solid

to liquid or from liquid to gaseous), of one gram/

kilogram of substance at constant temperature is

called latent heat (symbol L). Its unit is cal/g or

kcal/kg or J/kg.

The amount of heat absorbed or given out

during the change of state is given by : Q = ML,

where M is the mass of the substance.

Latent heat is of two types : (i) Latent heat

of fusion for change from solid to liquid at the

melting point and (ii) Latent heat of vapourisation

for change of state from liquid to gaseous state

at boiling.

* Latent heat of fusion of ice is 80 cal/g.

* Latent heat of vapourisation for water is

536 cal/g.

* Latent heat is used for doing work in

increasing the distance between the molecules

during the change of state. That is, the latent heat

increases the potential energy of molecules and

their kinetic energy remains constant, therefore,

the temperature also remains constant.





Assumption of Kinetic Theory of Gases and Gas

Equation

1. If N be the Avogadro's number and R be the gas

constant, then Boltzmann constant is given by :

a) RN b) R

N

c) N

Rd)

1

RN

2. In the kinetic theory of gases, it is assumed that

the gas molecules :

a) repel each other

b) collide elastically

c) move with uniform velocity

d) are massless particles

3. Which of the following is NOT an assumption of

kinetic theory of gases ?

a) All molecules of a gas are identical

b) Gas molecules are like rigid balls

c) All gases are perfect gases

d) Duration of molecular collision is negligible

4. What is a perfect gas ?

a) One that consists of molecules

b) Gas satisfying assumption of kinetic theory

c) A gas having Maxwellian distribution of speed

d) Gas consisting of massless particles

5. In kinetic theory of gases, it is assumed that

molecular collisions are :

a) inelastic

b) for negligible duration

c) one dimensional (head on)

d) unable to exert mutual force

6. Which of the following is NOT the property of

Brownian motion ?

The Brownian motion is :

a) continuous

b) random

c) due to molecular collision with the walls

d) regular

7. NTP corresponds to a temperature of :

a) OK b) – 273 K

c) 273 K d) none of the above

MULTIPLE CHOICE QUESTIONS

8. In the gas equation PV = RT, the V refers to the

volume of :

a) any amount of gas

b) one gram of gas

c) one mole of gas

d) one kilogram of gas

9. Which of the following phenomenon cannot be

explained using the kinetic theory of gases ?

a) Brownian motion

b) Maxwell's law of distribution of velocities

c) Evaporation

d) Viscosity

10. The molecular motion ceases at :

a) 273 K b) 2730C

c) – 273 K d) – 2730C

11. A closed bottle containing water is opened on the

moon. What will happen ?

a) The water will freeze

b) The water will boil

c) The water will remain as before

d) The water will decompose into H2 and O

2

12. Given that R is the molar gas constant and N is

the Avogadro's number, then R

N gives :

a) Planck's constant

b) Boltzmann's constant

c) Stefan's constant

d) None of the above

13. Gases deviate from perfect gas behaviour because

their molecules :

a) are polyatomic

b) do not attract each other

c) interact with each other through inter molecular

forces

d) are of very small size

14. When does a gas behave like perfect gas ?

a) At high pressure and high temperature

b) At low pressure and low temperature

c) At high pressure and low temperature

d) At low pressure and high temperature





15. A gas is compressed at constant temperature.

Its molecules gain :

a) speed b) kinetic energy

c) internal energy d) none of the above

16. At constant pressure the rms velocity 'c' is related

to density 'd' as :

a) c d b) 1

cd

c) c d d) 1

cd

17. Two gases A and B having the same temperature

T, same pressure p and same volume V are

mixed. If the temperature of the mixture remains

unchanged and the volume occupied by it is V

2

then the pressure of the mixture will be :

a) p / 2 b) p

c) 2 p d) 4 p

18. A cylinder contains 2 kg of air at a pressure

105 Pa. If 2 kg more air is pumped into it, keeping

the temperature constant, the pressure will be :

a) 105 Pa b) 2 105 Pa

c) 0.5 105 Pa d) 1010 Pa

19. Two gases at the same temperature T, pressure

P and volume V are mixed. The mixture has

volume V, & temperature T. What is the pressure

of the mixture ?

a) P

2b) P

c) 2 P d) 4 P

20. What causes Maxwellian distribution of molecular

speed ?

a) Spherical shape of the molecules

b) Elastic nature of the molecular collision

c) Small size of the molecules



T, same pressure p and same volume V are

mixed. If the temperature of the mixture remains

unchanged and the volume occupied by it is V,

then the pressure of the mixture will be :

a) p / 2 b) p

c) 2 p d) 4 p

22. One mole of a gas at a pressure 2 Pa and

temperature 270C is heated till both pressure and

volume are doubled. What is the temperature of

the gas ?

a) 300 K b) 600 K

c) 900 K d) 1200 K

23. Two substances of densities P1 and P

2 are mixed

in equal volume and the relative density of the

mixture is 4. When they are mixed in equal

masses, the relative density of the mixture is 3.

What are the values of 1 and

2?

a) 1 = 6 and

2 = 2

b) 1 = 3,

2 = 5

c) 1 = 12,

2 = 4


24. 32 g of oxygen, 14 g of nitrogen, 22 g of carbon

dioxide are mixed in an enclosure. The final

volume is 6 litre. What is the pressure of the gas ?

Take R = 8.3 J mol–1 K–1, and temperature of the

gas 270C.

a) 0.6 106 Pa b) 0.32 106 Pa

c) 0.83 106 Pa d) none of the above

25. The volume of an enclosure is 3 litres. It contains

16 g of O2, 7 g of N

2 and 11 g of CO

2 at 270C.

What is the pressure exerted by the gases ?

a) 8.3 atm b) 4.2 atm

c) 2.1 atm d) 1 atm

26. The air density at Mount Everest is less than that

at the sea level. It is found by mountaineers that

for one trip lasting a few hours, the extra oxygen

needed by them corresponds to 30,000 cc at sea

level (pressure 1 atmosphere, temperature 270C).

Assuming that the temperature around Mount

Everest is –1300C and that the oxygen cylinder

has capacity of 5.2 litre, the pressure at which

oxygen be filled (at site) in the cylinder is :

a) 2.75 atm b) 5.5 atm

c) 8.25 atm d) 11 atm

Pressure of a Gas & Kinetic Energy

27. The kinetic energy of molecular motion appears

as :

a) potential energy

b) heat

c) temperature

d) none of the above





28. Kinetic theory of gases shows that at given

temperature the molecules of all the gases have

same mean :

a) speed b) velocity

c) momentum d) kinetic energy

29. The expression for pressure of gas and the gas

equation shows that the absolute temperature of

a gas is proportional to the average :

a) sum of vibrational, translational and rotational

kinetic energies of molecules

b) translational kinetic energy of molecules

c) rotational kinetic energy of molecules

d) vibrational kinetic energy of molecules

30. The kinetic energy of the diatomic molecules is

zero at :

a) 2730C b) – 2730C

c) 273 K d) – 273 K

31. The increase in the mass of the gas in a container

increases its pressure. Increase in which of the

following causes it ?

a) Only the momentum of molecules

b) Only the frequency of collision of molecules

c) Both momentum and frequency of collision

of molecules

d) Neither momentum nor frequency of collision

of molecules

32. The pressure of a gas is proportional to :

a) the sum of kinetic and potential energies

b) potential energy

c) kinetic energy


33. A gas molecule of mass m is incident normally

on the wall of the containing vessel with velocity

u. After the collision the momentum of the

molecule will be :

a) zero b) 1

2 mu

c) mu d) 2 mu

34. A cylinder contains 2 kg of air at a pressure

105 Pa. If 1 kg air pumped out of it, keeping the

temperature constant, the pressure will be :

a) 105 Pa b) 2 105 Pa

c) 0.5 105 Pa d) 1010 Pa

35. 'P' is the pressure and 'd' is the density of gas at

constant temperature, then :

a) P d b) 1

Pd

c) P d d) P 1 d

36. The pressure of a gas at constant volume is

proportional to :

a) total energy of the gas

b) average potential energy of the molecule

c) average kinetic energy of the molecule

d) total internal energy of gas

37. Hydrogen & nitrogen are at the same temperature.

The molecules of which one of them will have

more average kinetic energy ?

a) Hydrogen

b) Nitrogen

c) Both have equal amount of energy

d) Depends upon actual value of temperature

38. The r.m.s. speed of the molecules of a gas at a

pressure 105 Pa & temperature 00C is 0.5 km s–1.

If the pressure is kept constant but temperature

is raised to 8190C, the velocity will become :

a) 1 km s–1 b) 1.5 km s–1

c) 2 km s–1 d) 5 km s–1

39. The root mean square velocity of a gas molecules

is 10 km s–1. The gas is heated till its pressure

becomes 4 times. The velocity of the gas molecules

will now be :

a) 10 km s–1 b) 20 km s–1

c) 40 kms–1 d) 80 km s–1

40. A cubical vessel of side 1 m contains 6 1029

molecules of a gas per cubic metre. The mass of

each molecule is 5 10–27 kg. If the molecules

are moving with an average velocity of 1 km s–1,

what is the pressure of the gas ?

a) 103 Pa b) 105 Pa

c) 107 Pa d) 109 Pa

41. The density of hydrogen is 0.09 km m–3. What is

its root mean square velocity at NTP ?

a) 110

ms3

b)

110 km s

3

c) 110

ms3

d) 110

kms3





42. The molecules of a given mass of gas has a root

mean square velocity of 200 ms–1 at 270C and

1.0 105 Nm–2 pressure. When the temperature

is 1270C and pressure 0.5 105 Nm–2 the root

mean square velocity in ms–1 is :

a) 400

3b) 100 2

c) 2

1003

d) 50 2

3

43. The average kinetic energy of a hydrogen

molecule at 270C is 6.2 10–21 joule. The mass

of the hydrogen molecule is 3.1 10–27 kg. The

average kinetic energy at 1270C is :

a) 4.13 10–21 joule

b) 5.2 10–21 joule

c) 8.27 10–21 joule

d) 2.6 10–21 joule

Specific heats of Gases

44. In SI, Cp and C

are related as :

a) p

RC C

J b)

p

RC C

J

c) pC C R d)

pC C R

45. The molar specific heat at constant pressure (Cp)

for a monoatomic gas is :

a) 3

R2

b) 5

3

c) 7

5d) none of the above

46. The ratio of specific heats pC

C

for monoatomic

gases is :

a) 3

2b)

5

3

c) 7

5d) none of the above

47. The molar specific heat at constant pressure Cp

is related to internal energy U and absolute

temperature T as :

a) U

Tb)

dU

dT

c) dU

RdT


48. One mole of monoatomic gas 5

3

is mixed

with one mole of diatomic gas 7

5 . The value

of for the mixture is :

a) 4 b) 3

c) 2 d) 1.5

49. An ideal gas is heated isobarically. What fraction

of the heat supplied will be used to increase the

internal energy of the gas ?

a) 1

5b)

2

5

c) 3

5d)

4

5

50. If one mole of a monoatomic gas 5

3

is

mixed with one mole of a diatomic gas 7

,5

the value of for the mixture is :

a) 1.40 b) 1.50

c) 1.53 d) 3.07

51. If CV represents the molar specific heat at constant

volume of a gas, U represents the internal energy

and T is absolute temperature, then CV is given

by :

a) U

Tb)

dU

dT

c) dU

RdT


52. The molar specific heat at constant pressure Cp

is related to internal energy U and absolute

temperature T as :

a) U

Tb)

dU

dT

c) dU

RdT






53. Supposing the distance between the atoms of a

diatomic gas to be constant, its specific heat at

constant volume per mole (gram mole) is :

a) 5

R2

b) 3

R2

c) R d) 1

R2

54. The ratio P

V

C

C

of the specific heats at a

constant pressure and constant volume of any

perfect gas :

a) cannot be greater than 5/4

b) cannot be greater than 3/2

c) cannot be greater than 5/3

d) can have any value

Gas Laws

55. Which of the following laws can be the basis of

separating a mixture of gases ?

a) Avogadro's law

b) Graham's law of diffusion

c) Boyle's law d) Charle's law

56. Under same temperature and pressure, the rate

of diffusion (R) of a gas is related to the density

of the gas as :

a) 1

Rd

b) R d

c) 1

Rd

d) R d

57. In the Boyle's law relation PV = k, the value of k

depends on :

a) nature of gas b) pressure of gas

c) amount of gas s) none of the above

58. The air at 270C is pumped into a tyre to a pressure

of 8 atm. If the tyre bursts, what will be the drop

in temperature ? [Take ; = 1.5]

a) – 150°C b) – 123°C

c) 150°C d) 123°C

59. A flask containing air at 7°C at atmospheric

pressure is corked up. A pressure of 2.5 atmosphere

inside the flask would force the cork out. The

temperature at which it will happen is :

a) 147 °C b) 427 °C

c) 420 °C d) 700 °C

60. 200 cc of a gas is compressed to 100 cc at the

atmospheric pressure of 106 dyn/cm2. If the

change is sudden, what is the final pressure ?

[Given ; = 1.4]

a) 1.6 106 dyn/cm2

b) 2.0 106 dyn/cm2

c) 2.6 106 dyn/cm2

d) 3.0 l06 dyn/cm2

61. 300 cm3 of gas at 27°C is cooled to –3°C at

constant pres ure. The final volume is :

a) 300 cm3 b) 270 cm3

c) 150 cm3 d) 135 cm3

Recent Questions from MH-CET 2010

62. The mean kinetic energy of one gm-mole of a

perfect gas at absolute temperature T is :

a) 1

T2

b) 1

RT2

c) 2

kT3

d) 3

RT2

63. The real gases do not obey perfect gas equation

at :

a) low temperature and high pressure

b) high temperature and low pressure

c) low temperature and low pressure

d) high pressure and high temperature

64. The difference between the principal specific

heats of Nitrogen is 300 J/kg 0K and ratio of the

two specific heats is 1.4. The Cp is :

a) 1050 J/kg 0K

b) 650 J/kg 0K

c) 750 J/kg 0K

d) 150 J/kg 0K

65. When a gas enclosed in a vessel is heated through

10C, its pressure increases by 0.5%. The initial

temperature of the gas will be :

a) 200 K b) 200 °C

c) 2000 K d) 2000 °C

66. The average K.E. of a molecule of a gas at

absolute temperature T is proportional to :

a) 1 / T b) T

c) T d) T2





67. The average K.E. of a gas molecule at a temperature

400 K (Boltzmann constant = 1.38 10–23 J/K)

is :

a) 6.21 10–21 J b) 8.28 10–21 J

c) 8.62 10–5 J d) 6.21 10–5 J

68. A container holds one-half mole of argon gas

(C

= 12.4 J/mole K) at N.T.P. Heat energy

needed to double the pressure of the gas is :

a) 1960 J b) 1690 J

c) 196 J d) 169 J

69. Specific heat of a gas in an isothermal process

is :

a) infinite b) zero

c) negative d) constant

70. A gas at a room temperature contains N molecules

having speeds, 1,

2,

3, ......

N. Consider the

two quantities :

N

i

i 1

1a

N

and N

2 2

i

i 1

1b

N

a) a b b) a > b

c) a = b d) a < b

71. Two soap bubbles with radii 3 cm & 4 cm combine

to form a bubble of larger radius R, under

isothermal condition. Then R is approximately

equal to :

a) (33 + 43)1/3 cm b) (32 + 42)1/2 cm

c) (33 + 43)1/2 cm d) (33 + 42)1/3 cm

72. Of the following properties of gas molecules, the

one that is same for all ideal gases at a particular

temperature is :

a) mass b) velocity

c) momentum d) kinetic energy

73. The r.m.s. velocity of oxygen molecules at 160C

is 476 m/s. The r.m.s. velocity of hydrogen molecules

at 1270C is :

a) 1120 m/s b) 1603 m/s

c) 1896 m/s d) 2240 m/s

74. The interstellar space is permeated with atomic

hydrogen (mass of H atom = 1.67 10–27 kg) at

a concentration of about one atom of hydrogen

per cubic centimetre. The temperature of the

interstellar space is about 3 K. The r.m.s. speed

of interstellar hydrogen atoms is approximately :

[Boltzmann constant, k = 1.38 10–23 J/K]

a) 27 m/s b) 270 m/s

c) 2700 m/s d) 11,200 m/s

75. The root mean square speed of hydrogen molecules

at 300 K is 1930 m/s. Then the root mean square

speed of oxygen molecules at 900 K will be :

a) 1930 3 m/s b) 838 m/s

c) 643 m/s d) 1930

m/s3

76. K.E. per unit volume is given by :

a) 3

E P2

b) 2

E P3

c) 21

E mv2

d) none of these

77. Real gases show markable deviation from that

of ideal gas behavior at :

a) high temperature and low pressure

b) low temperature and high pressure

c) high temperature and high pressure

d) low temperature and low pressure

78. When system is in chemical equilibrium :

a) its composition remains constant

b) its composition changes

c) composition may change

d) none of these

79. A gas expands adiabatically at constant pressure

such that its temperature 1

T .V

The value of

p

v

C

C of the gas is :

a) 1.30 b) 1.50

c) 1.67 d) 2.00

80. Which of the following is the unit of specific

heat ?

a) J kg 0C–1 b) J/kg 0C

c) kg 0C/J d) J kg 0C–2

81. The temperature of a certain gas increased from

270C to 1270C, the increase in energy is :

a)3

4 times initial value

b)4

3 times initial value

c) 100 times initial value

d) 27 times initial value





82. SI unit of 'b' Van der Waal's constant is :

a) Nm2 b) m3 K mol

c) m3/K mol d) K mol/m3

83. Latent heat of ice is :

a) less than external latent heat of fusion

b) more than external latent heat of fusion

c) equal to external latent heat of fusion

d) twice the external latent heat of fusion

84. If CP – C

V = R and P

V

C,

C then which relation

is correct ?

a) V

RC

1

b) V

RC

1

c) 2

V

RC

d)

V 2

1C

R

85. According to Kirchhoff's law of radiation which

of the following relation is correct ?

a) b aE E b)

b

EE

a

c) 2

bE E a d)

bE E a

86. Unit of Stefan's constant is given by :

a) W/m K2 b) W/m2 K4

c) W2/m2 K4 d) W/m K

87. Unit of 'b' in Van der Waal's equation is given

by :

a) m3 b) m2

c) mole/m d) m3/mole

88. In phasor diagram, Hoarfrost indicates conversion

of :

a) vapour to solid b) solid to vapour

c) liquid to vapour d) solid to liquid

89. If the volume of a gas (at constant temperature)

is reduced by 10%, then the percentage change

in the pressure is :

a) 11 % b) 22 %

c) 30 % d) 40 %

90.V

P

C

C is :

a) Less than 1 b) Greater than 1

c) Equal to 1 d) None of these

91. Work done against inter molecular forces of

attraction is :

a) Internal Latent Heat

b) External Latent Heat

c) Both

d) None

93. Kinetic energy per unit volume of a gas is E, then

the pressure exerted by the gas is :

a) 3

E2

b) 2

E3

c) 1

E3

d) E

93. Two gases have densities in the ratio 2 : 3 and

pressure exerted are in the ratio 3 : 2. Then the

ratio of their RMS velocity is :

a) 2 : 3 b) 3 : 2

c) 1 : 3 d) 6 : 8

94. At what temperature will the R.M.S. velocity of

a gas be double its value at N.T.P. ?

a) 273° C b) 546° C

c) 819° C d) 1092° C

95. The average distance covered by a molecule

between two successive collisions is called :

a) free path

b) constant path

c) mean free path

d) free path per unit time

96. KE per unit volume is E. The pressure exerted

by the gas is given by :

a) E

3b)

2E

3

c) 3E

2d)

E

2

97. The velocity of 4 gas molecules are given by

1 km/s, 3 km/s, 5 km/s and 7 km/s. Calculate the

difference between average and RMS velocity :

a) 0.338 b) 0.438

c) 0.583 d) 0.683

98. If a gas expands under isothermal conduction,

then what happen to rms velocity ?

a) increases b) decreases

c) remains constant d) can not be predicted





99. What will be r.m.s. speed of a gas at 800 K ?

a) four times the values at 2000 K

b) half the value at 2000 K

c) twice the value at 2000 K

d) same as at 2000 K

100. What temperature does the average translational

K.E. of a molecule in a gas becomes equal to

K.E. of an electron accelerated from rest through

potential difference of V volt ? All symbols have

their usual meaning.

a) 2eVN

3Rb)

3R

2eVN

c) NeV

Rd)

2NeV

R

101. Gases exert pressure on the walls of the container

because the gas molecules :

a) have finite volume

b) obey Boyle's law

c) possess momentum

d) collide with one another

102. The dimensions of Stefan's constant are :

a) [ M0 L1 T–3 K–4 ]

b) [ M1 L1 T–3 K–3 ]

c) [ M1 L2 T–3 K–4 ]

d) [ M1 L0 T–3 K–4 ]

103. In the expression for Boyle's law, the product 'PV'

has dimensions of :

a) force b) impulse

c) energy d) momentum

REVISION OUESTIONS

from Competitive Exams

1. We have a jar A filled with a gas characterised

by parameter p, V and T and another jar B with

a gas with parameters 2p, V/4 and 2T. Where

the symbols have their usual meaning. The ratio

of the number of molecules of jar A to those of

jar B is :

a) 1 : 1 b) 1 : 2

c) 2 : 1 d) 4 : 1

2. N molecules each of mass m of a gas A and 2 N

molecules each of mass 2 m of gas B are contained

in the same vessel which is maintained at

temperature T. The mean square velocity of

molecules of B type is 2 and the mean square

rectangular component of the velocity of A type

is denoted by 2. Then 2

2

:

a) 2 b) 1

c) 1

3d)

2

3

3. The value of densities of two diatomic gases at

constant temperature and pressure are d1 and d

2

then the ratio of speed of sound in these gases

will be :

a) 1 2d d b)

2

1

d

d

c) 1

2

d

dd)

1 2d d

4. Two quantities A and B have different dimension.

Which mathematical operation given below is

physically meaningful ?

a) A

Bb) A + B

c) A – B d) none

5. The dimension of 'a' in Van der Waal Gas equation,

2

aP (V b) RT

V

is :

a) 3 2ML T b)

5 2ML T

c) 2 1ML T d)

5 3ML T





6. If the molecular weights of two gases are M1

and M2, then at a given temperature the ratio of

their r.m.s. velocities C1 and C

2 will be :

a)

1/ 2

1

2

M

M

b)

1/ 2

2

1

M

M

c)

1/ 2

1 2

1 2

M M

M M

d)

1/ 2

1 2

1 2

M M

M M

7. The temperature of an ideal gas is increased

from 120 K to 480 K. If at 120 K, the root mean

square velocity of gas molecules is V, at 480 K

it becomes :

a) 4 V b) 2 V

c) V

2d)

V

4

8. R.M.S. velocity of a particle is C at pressure P.

If pressure is increased two times, then R.M.S.

velocity becomes :

a) 0.5 b) C

c) 2 C d) 3 C

9. At 270C, temperature, the kinetic energy of an

ideal gas is E1. If the temperature is increased to

3270C, then kinetic energy would be :

a) 1

E

2b)

1

2

E

V

c) V2E

1d) 2 E

1

10. Gas exerts pressure on the walls of the container

because :

a) gas has weight

b) gas molecules have momentum

c) gas molecules collide with each other

d) gas molecules collide with the walls of the

container

11. R.M.S. velocity of nitrogen molecules at N.T.P.

is :

a) 33 m/s b) 493 m/s

c) 517 m/s d) 546 m/s

12. The root mean square velocity of a gas molecule

of mass M at given temperature is proportional

to :

a) M0 b) M1

c) M d) 1

M

13. Two different gases of molecular masses M1 and

M2 are at the same temperature. What is the ratio

of their mean square speeds ?

a) 1

2

M

Mb)

2

1

M

M

c) 1

2

M

Md)

2

1

M

M

14. A vessel of volume 0.1 m3 containing air at a

pressure of 76 cm of Hg is connected to an

evacuated vessel of capacity 0.09 m3. What is

the resultant air pressure if temperature is

assumed to remain constant ?

a) 40 cm of Hg

b) 45 cm of Hg

c) 52 cm of Hg

d) 76 cm of Hg


T, same pressure P and volume V are mixed. If

the mixture is at the same temperature and

occupies a volume V, the pressure of the mixture

is :

a) P b) 2 P

c) 4 P d) 6 P

16. The value of CV for one mole of neon gas is :

a) 1

R2

b) 3

R2

c) 5

R2

d) 7

R2

17. If R is gas constant of 1 gram mole, CP and C

V

are specific heat for a gas, then :

a) CP

– CV

= R b) CP – C

V < R

c) CP – C

V = 0 d) C

P – C

V > R

18. 70 calories of heat is required to increase the

temperature of 2 moles of an ideal gas from 30°C

to 35°C at constant pressure. The amount of heat

required to increase the temperature of the same

gas through the same temperature range (30°C

to 35°C) at constant volume will be :

[(Gas constant R = 2 calorie/(mole K)]

a) 30 calories b) 50 calories

c) 70 calories d) 90 calories





19. 1 mole of a diatomic gas with 7

5 is mixed

with 1mole of a monoatomic gas with 5

,3

then

the value of for the resulting mixture is :

a) 7

5b)

2

5

c) 3

2d)

12

7

20. When an ideal gas is heated at constant pressure,

the fraction of the heat energy supplied which

increases the internal energy of the gas is :

a) 2

5b)

3

5

c) 3

7d)

5

7

21. 1 mole of a mono atomic gas is first heated at

constant volume by 1000C. The change in internal

energy of the gas is U1. Next it is heated at

constant pressure by 1000C, the change in internal

energy of the gas is U2.

Then the ratio 1

2

U:

U

a) 1 b) 3

5

c) 5

3d) uncertain

22. 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 of

specific heat at constant pressure to that at

constant volume :

a) 3

2b)

23

15

c) 35

23d)

4

3

23. The quantity of heat required to heat 1 mole of a

monoatomic gas through one degree K at constant

pressure is :

a) 3.5 R b) 2.5 R

c) 1.5 R d) none of these

24. Boiling water is changing into steam under this

condition, the specific heat of water is :

a) one b) 0

c) d) < 1

25. Water is used to cool the radiators of engines in

cars because :

a) of its low boiling point

b) of its high specific heat

c) of its low density

d) of its easy availability

26. The latent heat of vapourisation of water is 2240 J.

If the work done in the process of vapourisation

of 1 g is 168 J, then increase in internal energy

is :

a) 2408 J b) 2240 J

c) 2072 J d) 1904 J

27. The latent heat of vapourization of water is 538

cal/gram. The work done in this process of expansion

is 168 Joules. The increase in internal energy is :

a) 370 cal b) 498 cal

c) 249 cal d) 706 cal

28. The ratio of specific heats for oxygen is 1.4.

Density of oxygen at S.T.P. = 1.44 kg/m3.

If atmospheric pressure is 1.013 105 N/m3,

the specific heat at constant volume is :

a) 257.7 J kg–1 K–1

b) 644.3 J kg–1 K–1

c) 8.36 J kg–1 K–1

d) 901.2 J kg–1 K–1

29. Specific heat constant of aluminium is greater than

that of copper. When two balls of same mass

and radius of respective elements is submerged

in a hot liquid, then at equilibrium :

a) temperature of aluminium ball is greater than

that of copper

b) both have same temperature

c) temperature of iron ball is greater than that of

aluminium ball

d) none of these





30. 2 kg ice at –20°C is mixed with 5 kg of water at

20°C in an insulating vessel having a negligible

heat capacity. Calculate the final mass of water

remaining in the container. It is given that the

specific heats of water and ice are 1 kcal/kg/0C

and 0.5 kcal/kg/0C while the latent heat of fusion

of ice is 80 kcal/kg :

a) 7 kg b) 6 kg

c) 4 kg d) 2 kg

31. Three perfect gases at absolute temperature T1,

T2 and T

3 are mixed. The masses of molecules

are m l, m

2 and m

3 and the number of molecules

are n1, n

2 and n

3 respectively. Assuming no loss

of energy, the final temperature of the mixture

is :

a)

2 2 2 2 2 2

1 1 2 2 3 3

1 1 2 2 3 3

n T n T n T

n T n T n T

b)1 2 3(T T T )

3

c)1 1 2 2 3 3

1 2 3

n T n T n T

n n n

d)

2 2 2

1 1 2 2 3 3

1 1 2 2 3 3

n T n T n T

n T n T n T

32. In the given (V – T) diagram, what is the relation

between pressures P1 and P

2 :

a) P2 < P

1b) Cannot be predicted

c) P2 = P

1d) P

2 > P

1

33. The amount of heat energy req uired to raise the

temperature of 1 g of Helium at NTP, from T1K

to T2K is :

a) a B 2 1

3N k (T T )

4 b)

2a B

1

T3N k

4 T

c) a B 2 1

3N k (T T )

8 d) a B 2 1

3N k (T T )

2

34. The molar specific heats of an ideal gas at

constant pressure and volume are denoted by Cp

and Cv, respectively. If

p

v

C

C and R is the

universal gas constant, then Cv is equal to :

a) ( 1)

R

b) R

c) 1

1

d) R

( 1)

35. Two non-reactive monoatomic ideal gases have

their atomic masses in the ratio 2 : 3. The ratio of

the partial pressures, when enclosed in a 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

36. The two ends of a metal rod are maintained at

temperatures 1000C and 1100C. The rate of heat

flow in the rod is found to be 4.0 J/s. If the ends

are maintained at temperatures 2000C and 2100C,

the rate of heat flow will be :

a) 8.0 J/s b) 4.0 J/s

c) 44.0 J/s d) 16.8 J/s

37. The ratio of the specific heats p

v

C

C in terms

of degrees of freedom (n) is given by :

a) 2

1n

b) n

12

c) 1

1n

d) n

13

38. A Carnot engine, having an efficiency of 1

10

as heat engine, is used as a refrigerator. If the

work done on the system is 10 J, the amount of

energy absorbed from the reservoir at lower

temperature is :

a) 90 J b) 1 J

c) 100 J d) 99 J

39. One mole of an ideal diatomic gas undergoes a

transition from A to B along a path AB as shown

in the figure.





The change in internal energy of the gas during

the transition is :

a) 20 J b) – 12 kJ

c) 20 kJ d) – 20 kJ

40. On observing light from three different stars P, Q

and R, it was found that intensity of violet colour

is maximum in the spectrum of P, the intensity of

green colour is maximum in the spectrum of R

and the intensity of red colour is maximum in the

spectrum of Q. If TP, T

Q & T

R are the respective

absolute temperatures of P, Q and R, then it can

be concluded from the above observations that :

a) P R QT T T b) P Q R

T T T

c) P Q RT T T d) P R Q

T T T

41. Figure below shows two paths that may be taken

by a gas to go from a state A to a state C.

In process AB, 400 J of heat i added to the system

and in process BC, 100 J of heat is added to the

system. The heat absorbed by the system in the

process AC will be :

a) 460 J b) 300 J

c) 380 J d) 500 J

42. Consider an ideal gas confined in an isolated closed

chamber. As the gas undergoes an adiabatic

expansion, the average time of collision between

molecules increases as Vq, where V is the volume

of the gas.

The value of q is p

v

C

C

:

a) 1

2

b)

1

2

c) 3 5

6

d)

3 5

6

43. A solid body of constant heat capacity 1 J/0C is

being heated by keeping it in contact with

reservoirs in two ways :

i) Sequentially keeping in contact with 2 reservoirs

such that each reservoir supplies same amount

of heat.

ii) Sequentially keeping in contact with 8 reservoirs

such that each reservoir supplies same amount

of heat.

In both the cases body is brought from initial

temperature l000C to final temperature 2000C.

Entropy change of the body in the two cases

respectively is :

a) In2, 2 In2 b) 2 In2, 8 In2

c) In2, 4 In2 d) In2, In2

44. Consider a spherical shell of radius R at temperature

T. The black body radiation inside it can be

considered as an ideal gas of photons with internal

energy per unit volume 4U

u TV

and pressure

1 Up .

3 V

If the shell now undergoes an

adiabatic expansion, the relation between T and

R is :

a) 1

TR

b) 3

1T

R

c) RT e d) 3RT e45. 4.0 g of a gas occupies 22.4 litres at NTP. The

specific heat capacity of the gas at constant volume

is 5.0 JK–1 mol–1. If the speed of sound this gas

at NTP is 952 ms–1 then the heat capacity at constant

pressure is :

[Take gas constant, R = 8.3 JK–1 mol–1]

a) 7.0 JK–1 mol–1 b) 8.5 JK–1 mol–1

c) 8.0 JK–1 mol–1 d) 7.5 JK–1 mol–1

46. Two vessels separately contain two ideal gases

A and B at the same temperature, the pressure

of A being twice that of B. Under such conditions,

the density of A is found to be 1.5 times the density

of B. The ratio of molecular weight of A and B

is :





a) 2 b) 1

2

c) 2

3d)

3

4

47. An ideal gas is compressed to half its initial volume

by means of several processes. Which of the

process results in the maximum work done on

the gas ?

a) Isochoric b) Isothermal

c) Adiabatic d) Isobaric

Brain Teasers

1. A gas at a pressure p is contained in a vessel. If

the masses of all the molecules are halved and

their velocities are doubled, then the resulting

pressure of the gas will be :

a) p

4b)

p

2

c) p d) 2 p

2. We have a sample of gas characterised by p, V

and T and another sample of gas characterised

by 2p, V/4 and 2T. What is the ratio of the

molecules in the first and second samples ?

a) 2 b) 4

c) 8 d) 16

3. In order to double the average separation between

the molecules of a sample of gas at constant

temperature the pressure should be reduced by a

factor :

a) 1 / 2 b) 1 / 4

c) 1 / 8 d) 1 / 16

4. A sample of oxygen have the same mass, volume

and pressure as another sample of hydrogen. The

ratio of their temperature will be :

T(oxygen)

/ T(hydrogen)

=

a) 4 b) 8

c) 16 d) 32

5. A mixture of two gases is contained in a vessel.

The gas-I is monoatomic and gas-II is diatomic

and ratio of their molecular masses 1

2

M 1.

M 4

What is the ratio of the root mean square speeds

of the molecules of two gases ?

a) 2 b) 4

c) 8 d) 16

6. The temperature of gas is raised from 27°C to

90°C. What is the percentage increase in r.m.s.

velocity of the molecules ?

a) 10 % b) 15 %

c) 20 % d) 17.5 %

7. A container possesses gas at pressure 5 atm and

temperature 270C. If one-third of mass of gas is

removed and its temperature i raised by 600C,

what is the pressure of gas ?

a) 5 atm b) 2 atm

c) 4 atm d) 1 atm





8. A bottle open from above possess gas at 60°C.

To what temperature it should be heated so that

1th

4 mass of gas leaves it ?

a) 153 °C b) 171 °C

c) 444 °C d) 418 °C

9. What is the temperature at which r.m.s. velocity

of the gas molecules would become twice of its

value of 0 °C ?

a) 1000 °C b) 819 °C

c) 1400 °C d) 1200 °C

10. What is the r.m.s. speed of smoke particles at

NTP if mass of each particle is 5 10–17 kg ?

a) 1.5 cm/s b) 1.5 mm/s

c) 1.5 m/s d) 1.5 km/s

11. What is number moles of helium gas in the vessel

if its volume is 1.5 litre at temperature of 27°C

and 80 cm Hg pressure ?

a) 0.064 b) 640

c) 64 d) 0.64

12. Gas in a vessel is subjected to pressure of 20

atmosphere and temperature 27°C. What is the

pressure of gas if mass of gas is halved and

temperature is increased by 50°C ?

a) 18 atm b) 34 atm

c) 8.5 atm d) 11.67 atm

13. At temperature 30°C and atmospheric pressure

the volume of gas is 100 cm3. What temperature,

upto which it should be raised so that volume gets

doubled keeping the pressure same ?

a) 333 °C b) 606 °C

c) 15 °C d) 60 °C

14. Ideal gas obeys additional law VP2 = constant

during an experiment. If gas is initially at

temperature T and volume V, at what temperature

its volume becomes doubled ?

a) 2 T b) T

2

c) T d) 2 T

15. What is the r.m.s. velocity of the oxygen molecules

at a temperature for which hydrogen molecules

have rms velocity 2 km/s ?

a) 2 km/s b) 4 km/s

c) 0.5 km/s d) 0.25 km/s

16. What should be the increase in pressure to

decrease the volume of a gas by 5%, if temperature

remains constant ?

a) 4.26 % b) 5.26 %

c) 10 % d) 5 %



DINESH [MHT - CET] PHYSICS


01. (d)

02. (b)

03. (c)

07. (c)

08. (b)

11. (a)

12. (d)

Answer Key

MH Text Book Based MCQ's

01. (b)

02. (b)

03. (c)

04. (b)

05. (b)

06. (d)

07. (c)

08. (c)

09. (d)

10. (d)

11. (b)

12. (b)

13. (c)

14. (d)

15. (d)

16. (d)

17. (c)

18. (b)

19. (c)

20. (d)

21. (c)

22. (d)

23. (a)

24. (c)

25. (a)

26. (a)

27. (c)

28. (d)

29. (b)

30. (d)

31. (b)

32. (c)

33. (c)

34. (c)

35. (a)

36. (c)

37. (c)

38. (a)

39. (b)

40. (d)

41. (c)

42. (c)

43. (c)

44. (b)

45. (b)

46. (c)

47. (c)

48. (c)

49. (c)

50. (b)

51. (c)

52. (c)

53. (a)

54. (b)

55. (b)

56. (c)

57. (b)

58. (b)

59. (b)

60. (b)

61. (b)

62. (b)

63. (a)

64. (a)

65. (c)

66. (b)

67. (b)

68. (d)

69. (d)

70. (c)

71. (a)

72. (a)

73. (b)

74. (b)

75. (a)

76. (b)

77. (a)

78. (b)

79. (b)

80. (b)

81. (b)

82. (c)

83. (a)

84. (a)

85. (b)

86. (b)

87. (a)

88. (a)

89. (a)

90. (a)

91. (a)

92. (b)

93. (b)

94. (c)

95. (c)

96. (b)

97. (c)

98. (c)

99. (c)

100. (a)

101. (c)

102. (d)

103. (c)

REVISION QUESTIONS from Competitive Exams.

01. (d)

02. (b)

03. (a)

04. (b)

05. (b)

06. (b)

07. (b)

08. (b)

09. (d)

10. (b)

11. (b)

12. (d)

13. (a)

14. (a)

15. (b)

16. (b)

17. (b)

18. (b)

19. (c)

20. (d)

21. (b)

22. (b)

23. (b)

24. (c)

25. (c)

26. (c)

27. (b)

28. (b)

29. (d)

30. (b)

31. (c)

32. (a)

33. (c)

34. (d)

35. (d)

36. (b)

37. (a)

38. (a)

39. (d)

40. (d)

41. (a)

42. (a)

43. (d)

44. (a)

45. (c)

46. (d)

47. (c)

BRAIN TEASERS

04. (c)

05. (a)

06. (a)

09. (b)

10. (a)

13. (a)

14. (a)

15. (c)

16. (b)






Hints & Solutions 23



















Kinetic Theory of Gases

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