Kinetic Theory Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice questions.
Each question has 4 choices (a), (b), (c) and (d), out of which ONLY
ONE choice is correct.
Q.1 If pressure of a gas contained in a closed vessel is increased
by 0.4% when heated by 1°C, the initial temperature must
be
(a) 250 K (b) 250°C (c) 2500 K (d) 25°C
Q.2 To double the volume of a given mass of an ideal gas at
27°C keeping the pressure constant, one must raise the
temperature in degree centigrade to
(a) 54 (b) 270 (c) 327 (d) 600
Q.3 Under which of the following conditions is the law
PV RT = obeyed most closely by a real gas?
(a) High pressure and high temperature
(b) Low pressure and low temperature
(c) Low pressure and high temperature
(d) High pressure and low temperature
Q.4 The pressure P, volume V and temperature T of a gas in
the jar A and the other gas in the jar B at pressure 2 P ,
volume 
4
V
 and temperature  2T,  then the ratio of, the
number of molecules in the jar A and B will be
(a) 1 : 1 (b) 1 : 2
(c) 2 : 1 (d) 4 : 1
Q.5 A flask is filled with 13 gm of an ideal gas at 27°C and its
temperature is raised to 52°C. The mass of the gas that has
to be released to maintain the temperature of the gas in
the flask at 52°C and the pressure remaining the same is
(a) 2.5 g (b) 2.0 g (c) 1.5 g (d) 1.0 g
Page 2


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice questions.
Each question has 4 choices (a), (b), (c) and (d), out of which ONLY
ONE choice is correct.
Q.1 If pressure of a gas contained in a closed vessel is increased
by 0.4% when heated by 1°C, the initial temperature must
be
(a) 250 K (b) 250°C (c) 2500 K (d) 25°C
Q.2 To double the volume of a given mass of an ideal gas at
27°C keeping the pressure constant, one must raise the
temperature in degree centigrade to
(a) 54 (b) 270 (c) 327 (d) 600
Q.3 Under which of the following conditions is the law
PV RT = obeyed most closely by a real gas?
(a) High pressure and high temperature
(b) Low pressure and low temperature
(c) Low pressure and high temperature
(d) High pressure and low temperature
Q.4 The pressure P, volume V and temperature T of a gas in
the jar A and the other gas in the jar B at pressure 2 P ,
volume 
4
V
 and temperature  2T,  then the ratio of, the
number of molecules in the jar A and B will be
(a) 1 : 1 (b) 1 : 2
(c) 2 : 1 (d) 4 : 1
Q.5 A flask is filled with 13 gm of an ideal gas at 27°C and its
temperature is raised to 52°C. The mass of the gas that has
to be released to maintain the temperature of the gas in
the flask at 52°C and the pressure remaining the same is
(a) 2.5 g (b) 2.0 g (c) 1.5 g (d) 1.0 g
2
DPP/ P 26
Q.6 The pressure and temperature of two different gases is
P
and T having the volume 
V
for each. They are mixed
keeping the same volume and temperature, the pressure of
the mixture will be
(a)
/2 P
(b)
P
(c)
2P
(d)
4P
Q.7 The root mean square velocity of a gas molecule of mass
m at a given temperature is proportional to
(a) m
o
(b) m (c) m (d)
1
m
Q.8 Which of the following statements is true?
(a) Absolute zero temperature is not zero energy
temperature
(b) Two different gases at the same temperature and
pressure have equal root mean square velocities
(c) The root mean square speed of the molecules of
different ideal gases, maintained at the same
temperature are the same
(d) Given sample of 1 cc of hydrogen and 1 cc of oxygen
both at NTP; oxygen sample has a large number of
molecules
Q.9 At room temperature, the r .m.s. speed of the molecules of
certain diatomic gas is found to be 1930 m/s. The gas is
(a)
2
H (b)
2
F (c)
2
O (d)
2
Cl
Q.10 Root mean square velocity of a particle is v at pressure P.
If pressure is increased two times, then the r .m.s. velocity
becomes
(a) 2 v (b) 3 v (c) 0.5 v (d) v
Q.11 In the two vessels of same volume, atomic hydrogen and
helium at pressure 1 atm and 2 atm are filled. If temperature
of both the samples is same, then average speed of
hydrogen atoms 
H
C <> will be related to that of helium
He
C <> as
(a) 2
H He
CC < >= <> (b)
H He
CC < >=<>
(c) 2
H He
CC < >=<> (d)
2
He
H
C
C
<>
< >=
Q.12 For a gas at a temperature T the root-mean-square velocity
,
rms
v the most probable speed 
mp
v
, and the average speed
u a
v obey the relationship
(a)
u
>>
a rms mp
v vv
(b)
u
>>
rms a mp
v vv
(c)
u
>>
mp a rms
v vv
(d)
u
>>
mp rms a
v vv
Q.13 One mole of ideal monoatomic gas ( 5 / 3) g= is mixed with
one mole of diatomic gas ( 7/ 5) g= . What is g for the
mixture? 
Cp
Cv
æö
g=
ç÷
èø
(a) 3/2 (b) 23/15 (c) 35/23 (d) 4/3
Q.14The value of the gas constant (R) calculated from the
perfect gas equation is 8.32 Joule/gm mol K , whereas its
value calculated from the knowledge of C
p
 and C
V
 of the
gas is 1.98 cal/gm mole K . From this data, the value of J
is
(a) 4.16 J / cal (b) 4.18 J / cal
(c) 4.20 J / cal (d) 4.22 J / cal
Q.15 Gas at a pressure 
0
P is contained in a vessel. If the masses
of all the molecules are halved and their speeds are
doubled, the resulting pressure 
P
will be equal to
(a)
0
4P (b) 
0
2P (c) 
0
P (d)
0
2
P
Q.16 The relation between the gas pressure P and average kinetic
energy per unit volume E is
(a)
1
2
PE =
(b)
PE =
(c)
3
2
PE =
(d)
2
3
PE =
Q.17 Mean kinetic energy (or average energy) per gm molecule
of a monoatomic gas is given by
(a)
3
2
RT (b)
1
2
KT (c)
1
2
RT (d)
3
2
KT
Q.18 At which of the following temperature would the molecules
of a gas have twice the average kinetic energy they have at
20°C?
(a) 40C
o
(b) 80C
o
(c) 313C
o
(d) 586 C
o
Page 3


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice questions.
Each question has 4 choices (a), (b), (c) and (d), out of which ONLY
ONE choice is correct.
Q.1 If pressure of a gas contained in a closed vessel is increased
by 0.4% when heated by 1°C, the initial temperature must
be
(a) 250 K (b) 250°C (c) 2500 K (d) 25°C
Q.2 To double the volume of a given mass of an ideal gas at
27°C keeping the pressure constant, one must raise the
temperature in degree centigrade to
(a) 54 (b) 270 (c) 327 (d) 600
Q.3 Under which of the following conditions is the law
PV RT = obeyed most closely by a real gas?
(a) High pressure and high temperature
(b) Low pressure and low temperature
(c) Low pressure and high temperature
(d) High pressure and low temperature
Q.4 The pressure P, volume V and temperature T of a gas in
the jar A and the other gas in the jar B at pressure 2 P ,
volume 
4
V
 and temperature  2T,  then the ratio of, the
number of molecules in the jar A and B will be
(a) 1 : 1 (b) 1 : 2
(c) 2 : 1 (d) 4 : 1
Q.5 A flask is filled with 13 gm of an ideal gas at 27°C and its
temperature is raised to 52°C. The mass of the gas that has
to be released to maintain the temperature of the gas in
the flask at 52°C and the pressure remaining the same is
(a) 2.5 g (b) 2.0 g (c) 1.5 g (d) 1.0 g
2
DPP/ P 26
Q.6 The pressure and temperature of two different gases is
P
and T having the volume 
V
for each. They are mixed
keeping the same volume and temperature, the pressure of
the mixture will be
(a)
/2 P
(b)
P
(c)
2P
(d)
4P
Q.7 The root mean square velocity of a gas molecule of mass
m at a given temperature is proportional to
(a) m
o
(b) m (c) m (d)
1
m
Q.8 Which of the following statements is true?
(a) Absolute zero temperature is not zero energy
temperature
(b) Two different gases at the same temperature and
pressure have equal root mean square velocities
(c) The root mean square speed of the molecules of
different ideal gases, maintained at the same
temperature are the same
(d) Given sample of 1 cc of hydrogen and 1 cc of oxygen
both at NTP; oxygen sample has a large number of
molecules
Q.9 At room temperature, the r .m.s. speed of the molecules of
certain diatomic gas is found to be 1930 m/s. The gas is
(a)
2
H (b)
2
F (c)
2
O (d)
2
Cl
Q.10 Root mean square velocity of a particle is v at pressure P.
If pressure is increased two times, then the r .m.s. velocity
becomes
(a) 2 v (b) 3 v (c) 0.5 v (d) v
Q.11 In the two vessels of same volume, atomic hydrogen and
helium at pressure 1 atm and 2 atm are filled. If temperature
of both the samples is same, then average speed of
hydrogen atoms 
H
C <> will be related to that of helium
He
C <> as
(a) 2
H He
CC < >= <> (b)
H He
CC < >=<>
(c) 2
H He
CC < >=<> (d)
2
He
H
C
C
<>
< >=
Q.12 For a gas at a temperature T the root-mean-square velocity
,
rms
v the most probable speed 
mp
v
, and the average speed
u a
v obey the relationship
(a)
u
>>
a rms mp
v vv
(b)
u
>>
rms a mp
v vv
(c)
u
>>
mp a rms
v vv
(d)
u
>>
mp rms a
v vv
Q.13 One mole of ideal monoatomic gas ( 5 / 3) g= is mixed with
one mole of diatomic gas ( 7/ 5) g= . What is g for the
mixture? 
Cp
Cv
æö
g=
ç÷
èø
(a) 3/2 (b) 23/15 (c) 35/23 (d) 4/3
Q.14The value of the gas constant (R) calculated from the
perfect gas equation is 8.32 Joule/gm mol K , whereas its
value calculated from the knowledge of C
p
 and C
V
 of the
gas is 1.98 cal/gm mole K . From this data, the value of J
is
(a) 4.16 J / cal (b) 4.18 J / cal
(c) 4.20 J / cal (d) 4.22 J / cal
Q.15 Gas at a pressure 
0
P is contained in a vessel. If the masses
of all the molecules are halved and their speeds are
doubled, the resulting pressure 
P
will be equal to
(a)
0
4P (b) 
0
2P (c) 
0
P (d)
0
2
P
Q.16 The relation between the gas pressure P and average kinetic
energy per unit volume E is
(a)
1
2
PE =
(b)
PE =
(c)
3
2
PE =
(d)
2
3
PE =
Q.17 Mean kinetic energy (or average energy) per gm molecule
of a monoatomic gas is given by
(a)
3
2
RT (b)
1
2
KT (c)
1
2
RT (d)
3
2
KT
Q.18 At which of the following temperature would the molecules
of a gas have twice the average kinetic energy they have at
20°C?
(a) 40C
o
(b) 80C
o
(c) 313C
o
(d) 586 C
o
DPP/ P 26
3
Q.19 The kinetic energy of one gram molecule of a gas at normal
temperature and pressure is (R 8.31J/mol K) =-
(a)
4
0.56 10 J ´ (b)
2
1.3 10 J ´
(c)
2
2.7 10 J ´ (d)
3
3.4 10 J ´
Q.2070 calories of heat are required to raise the temperature
of
2 moles of an ideal gas at constant pressure from 30°C to
35°C. The amount of heat required to raise the temperature
of same gas through the same range (30C
o
 to 35 C)
o
at
constant volume (R 2 cal/mol K) =
(a) 30 cal (b) 50 cal (c) 70 cal (d) 90 cal
Q.21A vessel contains a mixture of one mole of oxygen and
two moles of  nitrogen at 300 K . The ratio of the average
rotational kinetic energy per 
2
O molecule to that per 
2
N
molecule is
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) Depends on the moments of inertia of the two
molecules
DIRECTIONS (Q.22-Q.24) : In the following questions, more than
one of the answers  given are correct. Select the correct answers
and mark it according to the following codes:
Codes : (a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 From the following statements, concerning ideal gas at any
given temperature T, select the correct one(s)
(1) The coefficient of volume expansion at constant
pressure is same for all ideal gases
(2) In a gaseous mixture, the average translational kinetic
energy of the molecules of each component is same
(3) The mean free path of molecules increases with the
decrease in pressure
(4) The average translational kinetic energy per molecule
of oxygen gas is 3KT (K being Boltzmann constant)
Q.23 Let 
rms
v,v and 
p
v
 respectively denote the mean speed,
root mean square speed and most probable speed of the
molecules in an ideal monoatomic gas at absolute
temperature T, the mass of a molecule is m. Then
(1)
p rms
v vv <<
(2) The average kinetic energy of a molecule is  
2
p
3
mv
4
(3) No molecule can have speed greater than 
rms
2v
(4) No molecule can have speed less than 
p
v /2
Q.24 A gas in container A is in thermal equilibrium with another
gas in container B, both contain equal masses of the two
gases in the respective containers. Which of the follow-
ing can be true
(1)
A B AB
P P,VV =¹ (2)
A A BB
P V PV =
(3)
B AB
PA P,VV ¹= (4)
AB
AB
PP
VV
=
DIRECTIONS (Q.25-Q.27) : Read the passage given below and
answer the questions that follows :
A diathermic piston divides adiabatic cylinder of volume V
0
 into
two equal parts as shown in the figure. Both parts contain ideal
monoatomic gases. The initial pressure and temperature of gas
in left compartment are P
0
 and T
0
 while that in right compartment
are 2P
0
 and 2T
0
. Initially the piston is kept fixed and the system
is allowed to acquire a state of thermal equilibrium.
00
, PT
0 0
2 ,2 P T
Q.25 The pressure in left compartment after thermal equilibrium
is achieved is
(a) P
0
(b)
0
3
2
P
(c)
0
4
3
P (d) None of these
Page 4


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice questions.
Each question has 4 choices (a), (b), (c) and (d), out of which ONLY
ONE choice is correct.
Q.1 If pressure of a gas contained in a closed vessel is increased
by 0.4% when heated by 1°C, the initial temperature must
be
(a) 250 K (b) 250°C (c) 2500 K (d) 25°C
Q.2 To double the volume of a given mass of an ideal gas at
27°C keeping the pressure constant, one must raise the
temperature in degree centigrade to
(a) 54 (b) 270 (c) 327 (d) 600
Q.3 Under which of the following conditions is the law
PV RT = obeyed most closely by a real gas?
(a) High pressure and high temperature
(b) Low pressure and low temperature
(c) Low pressure and high temperature
(d) High pressure and low temperature
Q.4 The pressure P, volume V and temperature T of a gas in
the jar A and the other gas in the jar B at pressure 2 P ,
volume 
4
V
 and temperature  2T,  then the ratio of, the
number of molecules in the jar A and B will be
(a) 1 : 1 (b) 1 : 2
(c) 2 : 1 (d) 4 : 1
Q.5 A flask is filled with 13 gm of an ideal gas at 27°C and its
temperature is raised to 52°C. The mass of the gas that has
to be released to maintain the temperature of the gas in
the flask at 52°C and the pressure remaining the same is
(a) 2.5 g (b) 2.0 g (c) 1.5 g (d) 1.0 g
2
DPP/ P 26
Q.6 The pressure and temperature of two different gases is
P
and T having the volume 
V
for each. They are mixed
keeping the same volume and temperature, the pressure of
the mixture will be
(a)
/2 P
(b)
P
(c)
2P
(d)
4P
Q.7 The root mean square velocity of a gas molecule of mass
m at a given temperature is proportional to
(a) m
o
(b) m (c) m (d)
1
m
Q.8 Which of the following statements is true?
(a) Absolute zero temperature is not zero energy
temperature
(b) Two different gases at the same temperature and
pressure have equal root mean square velocities
(c) The root mean square speed of the molecules of
different ideal gases, maintained at the same
temperature are the same
(d) Given sample of 1 cc of hydrogen and 1 cc of oxygen
both at NTP; oxygen sample has a large number of
molecules
Q.9 At room temperature, the r .m.s. speed of the molecules of
certain diatomic gas is found to be 1930 m/s. The gas is
(a)
2
H (b)
2
F (c)
2
O (d)
2
Cl
Q.10 Root mean square velocity of a particle is v at pressure P.
If pressure is increased two times, then the r .m.s. velocity
becomes
(a) 2 v (b) 3 v (c) 0.5 v (d) v
Q.11 In the two vessels of same volume, atomic hydrogen and
helium at pressure 1 atm and 2 atm are filled. If temperature
of both the samples is same, then average speed of
hydrogen atoms 
H
C <> will be related to that of helium
He
C <> as
(a) 2
H He
CC < >= <> (b)
H He
CC < >=<>
(c) 2
H He
CC < >=<> (d)
2
He
H
C
C
<>
< >=
Q.12 For a gas at a temperature T the root-mean-square velocity
,
rms
v the most probable speed 
mp
v
, and the average speed
u a
v obey the relationship
(a)
u
>>
a rms mp
v vv
(b)
u
>>
rms a mp
v vv
(c)
u
>>
mp a rms
v vv
(d)
u
>>
mp rms a
v vv
Q.13 One mole of ideal monoatomic gas ( 5 / 3) g= is mixed with
one mole of diatomic gas ( 7/ 5) g= . What is g for the
mixture? 
Cp
Cv
æö
g=
ç÷
èø
(a) 3/2 (b) 23/15 (c) 35/23 (d) 4/3
Q.14The value of the gas constant (R) calculated from the
perfect gas equation is 8.32 Joule/gm mol K , whereas its
value calculated from the knowledge of C
p
 and C
V
 of the
gas is 1.98 cal/gm mole K . From this data, the value of J
is
(a) 4.16 J / cal (b) 4.18 J / cal
(c) 4.20 J / cal (d) 4.22 J / cal
Q.15 Gas at a pressure 
0
P is contained in a vessel. If the masses
of all the molecules are halved and their speeds are
doubled, the resulting pressure 
P
will be equal to
(a)
0
4P (b) 
0
2P (c) 
0
P (d)
0
2
P
Q.16 The relation between the gas pressure P and average kinetic
energy per unit volume E is
(a)
1
2
PE =
(b)
PE =
(c)
3
2
PE =
(d)
2
3
PE =
Q.17 Mean kinetic energy (or average energy) per gm molecule
of a monoatomic gas is given by
(a)
3
2
RT (b)
1
2
KT (c)
1
2
RT (d)
3
2
KT
Q.18 At which of the following temperature would the molecules
of a gas have twice the average kinetic energy they have at
20°C?
(a) 40C
o
(b) 80C
o
(c) 313C
o
(d) 586 C
o
DPP/ P 26
3
Q.19 The kinetic energy of one gram molecule of a gas at normal
temperature and pressure is (R 8.31J/mol K) =-
(a)
4
0.56 10 J ´ (b)
2
1.3 10 J ´
(c)
2
2.7 10 J ´ (d)
3
3.4 10 J ´
Q.2070 calories of heat are required to raise the temperature
of
2 moles of an ideal gas at constant pressure from 30°C to
35°C. The amount of heat required to raise the temperature
of same gas through the same range (30C
o
 to 35 C)
o
at
constant volume (R 2 cal/mol K) =
(a) 30 cal (b) 50 cal (c) 70 cal (d) 90 cal
Q.21A vessel contains a mixture of one mole of oxygen and
two moles of  nitrogen at 300 K . The ratio of the average
rotational kinetic energy per 
2
O molecule to that per 
2
N
molecule is
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) Depends on the moments of inertia of the two
molecules
DIRECTIONS (Q.22-Q.24) : In the following questions, more than
one of the answers  given are correct. Select the correct answers
and mark it according to the following codes:
Codes : (a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 From the following statements, concerning ideal gas at any
given temperature T, select the correct one(s)
(1) The coefficient of volume expansion at constant
pressure is same for all ideal gases
(2) In a gaseous mixture, the average translational kinetic
energy of the molecules of each component is same
(3) The mean free path of molecules increases with the
decrease in pressure
(4) The average translational kinetic energy per molecule
of oxygen gas is 3KT (K being Boltzmann constant)
Q.23 Let 
rms
v,v and 
p
v
 respectively denote the mean speed,
root mean square speed and most probable speed of the
molecules in an ideal monoatomic gas at absolute
temperature T, the mass of a molecule is m. Then
(1)
p rms
v vv <<
(2) The average kinetic energy of a molecule is  
2
p
3
mv
4
(3) No molecule can have speed greater than 
rms
2v
(4) No molecule can have speed less than 
p
v /2
Q.24 A gas in container A is in thermal equilibrium with another
gas in container B, both contain equal masses of the two
gases in the respective containers. Which of the follow-
ing can be true
(1)
A B AB
P P,VV =¹ (2)
A A BB
P V PV =
(3)
B AB
PA P,VV ¹= (4)
AB
AB
PP
VV
=
DIRECTIONS (Q.25-Q.27) : Read the passage given below and
answer the questions that follows :
A diathermic piston divides adiabatic cylinder of volume V
0
 into
two equal parts as shown in the figure. Both parts contain ideal
monoatomic gases. The initial pressure and temperature of gas
in left compartment are P
0
 and T
0
 while that in right compartment
are 2P
0
 and 2T
0
. Initially the piston is kept fixed and the system
is allowed to acquire a state of thermal equilibrium.
00
, PT
0 0
2 ,2 P T
Q.25 The pressure in left compartment after thermal equilibrium
is achieved is
(a) P
0
(b)
0
3
2
P
(c)
0
4
3
P (d) None of these
4
DPP/ P 26
Q.26The heat that flown from right compartment to left
compartment before thermal equilibrium is achieved is
(a)P
0
V
0
(b)
00
3
4
PV (c)
00
3
8
PV (d)
00
2
3
PV
Q.27 If the pin which was keeping the piston fixed is removed
and the piston is allowed to slide slowly such that a state
of mechanical equilibrium is achieved. The volume of left
compartment when piston is in equilibrium is
(a)
0
3
4
V (b)
0
4
V
(c)
0
2
V
 (d)
0
2
3
V
DIRECTIONS (Qs. 28-Q.30) : Each of these questions contains two
statements: Statement-1 (Assertion) and Statement-2 (Reason). Each
of these questions has four alternative choices, only one of which is
the correct answer. You have to select the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.28 Statement-1 : Internal energy of an ideal gas does not
depend upon volume of the gas.
Statement-2 : Internal energy of an ideal gas depends on
temperature of gas.
Q.29 Statement-1 : Equal masses of helium and oxygen gases
are given equal quantities of heat. There will be a greater
rise in the temperature of helium compared to that of
oxygen.
Statement-2 : The molecular weight of oxygen is more
than the molecular weight of helium.
Q.30Statement-1 : Maxwell speed distribution graph is
asymmetric about most probable speed.
Statement-2 : rms speed of ideal gas, depends upon it’s
type (monoatomic, diatomic and polyatomic).