Chapter 12
Kinetic Theory of Gases
1. One kg of diatomic gas is at a pressure of 5. The mass of a hydrogen molecule is 3.32 × 10–27
8 × 104 N/m2. The density of the gas is 4 kg/m3. kg. If 1023 hydrogen molecules strike, per second,
What is the energy of the gas due to its thermal a fixed wall of area 2 cm2 at an angle of 45° to
motion? [AIEEE-2009] the normal, and rebound elastically with a speed of
(1) 5 × 104 J (2) 6 × 104 J 103 m/s, then the pressure on the wall is nearly
[JEE (Main)-2018]
(3) 7 × 104 J (4) 3 × 104 J
(1) 2.35 × 103 N/m2 (2) 4.70 × 103 N/m2
2. An open glass tube is immersed in mercury in
such a way that a length of 8 cm extends above (3) 2.35 × 102 N/m2 (4) 4.70 × 102 N/m2
the mercury level. The open end of the tube is then 6. A mixture of 2 moles of helium gas (atomic mass
closed and sealed and the tube is raised vertically
= 4 u), and 1 mole of argon gas (atomic mass =
up by additional 46 cm. What will be length of the
40 u) is kept at 300 K in a container. The ratio of
air column above mercury in the tube now?
(Atmospheric pressure = 76 cm of Hg) Vrms (helium)
their rms speeds , is close to
[JEE (Main)-2014] Vrms (argon)
(1) 16 cm (2) 22 cm
[JEE (Main)-2019]
(3) 38 cm (4) 6 cm
(1) 2.24 (2) 0.45
3. Consider an ideal gas confined in an isolated
(3) 3.16 (4) 0.32
closed chamber. As the gas undergoes an
adiabatic expansion, the average time of collision 7. A 15 g mass of nitrogen gas is enclosed in a
between molecules increases as Vq, where V is vessel at a temperature 27°C. Amount of heat
the volume of the gas. The value of q is transferred to the gas, so that rms velocity of
molecules is doubled, is about [JEE (Main)-2019]
CP
[JEE (Main)-2015] [Take R = 83 J/K mole]
Cv
(1) 3 kJ (2) 14 kJ
3 5 3 5 (3) 10 kJ (4) 0.9 kJ
(1) (2)
6 6 8. Two kg of a monoatomic gas is at a pressure of
4 × 104 N/m2. The density of the gas is 8 kg/m3.
1 1 What is the order of energy of the gas due to its
(3) (4)
2 2 thermal motion ? [JEE (Main)-2019]
4. The temperature of an open room of volume 30 m3 (1) 103 J (2) 105 J
increases from 17°C to 27°C due to the sunshine.
The atmospheric pressure in the room remains (3) 104 J (4) 106 J
1 × 10 5 Pa. If n i and n f are the number of 9. A gas mixture consists of 3 moles of oxygen and
molecules in the room before and after heating, 5 moles of argon at temperature T. Considering
then nf – ni will be [JEE (Main)-2017] only translational and rotational modes, the total
(1) –1.61 × 1023 internal energy of the system is
(2) 1.38 × 1023 [JEE (Main)-2019]
(3) 2.5 × 1025 (1) 4 RT (2) 12 RT
(4) –2.5 × 1025 (3) 15 RT (4) 20 RT
Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : 011-47623456
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10. An ideal gas occupies a volume of 2 m 3 at a 16. The specific heats, CP and CV of a gas of diatomic
pressure of 3 × 106 Pa. The energy of the gas is molecules, A, are given (in units of J mol–1 K–1) by
[JEE (Main)-2019] 29 and 22, respectively. Another gas of diatomic
molecules, B, has the corresponding values 30 and
(1) 108 J (2) 9 × 106 J 21. If they are treated as ideal gases, then
(3) 6 × 104 J (4) 3 × 102 J
[JEE (Main)-2019]
11. An ideal gas is enclosed in a cylinder at pressure
(1) A is rigid but B has a vibrational mode
of 2 atm and temperature, 300 K. The mean time
between two successive collisions is 6 × 10–8 s. (2) A has a vibrational mode but B has none
If the pressure is doubled and temperature is (3) Both A and B have a vibrational mode each
increased to 500 K, the mean time between two
(4) A has one vibrational mode and B has two
successive collisions will be close to
17. A 25 × 10 –3 m 3 volume cylinder is filled with
[JEE (Main)-2019]
1 mol of O2 gas at room temperature (300 K). The
(1) 2 × 10–7 s (2) 3 × 10–6 s molecular diameter of O2, and its root mean square
(3) 0.5 × 10–8 s (4) 4 × 10–8 s speed, are found to be 0.3 nm and 200 m/s,
respectively. What is the average collision rate (per
12. If 10 22 gas molecules each of mass 10 –26 kg
second) for an O2 molecule? [JEE (Main)-2019]
collide with a surface (perpendicular to it)
elastically per second over an area 1 m2 with a (1) ~1012 (2) ~1010
speed 104 m/s, the pressure exerted by the gas (3) ~1011 (4) ~1013
molecules will be [JEE (Main)-2019]
18. A cylinder with fixed capacity of 67.2 lit contains
(1) 1 N/m2 (2) 2 N/m2 helium gas at STP. The amount of heat needed to
(3) 3 N/m2 (4) 4 N/m2 raise the temperature of the gas by 20°C is :
13. The temperature, at which the root mean square [Given that R = 8.31 J mol–1K–1]
velocity of hydrogen molecules equals their escape [JEE (Main)-2019]
velocity from the earth, is closest to (1) 700 J (2) 350 J
[Boltzmann constant kB = 1.38 × 10–23 J/K (3) 374 J (4) 748 J
Avogadro Number NA = 6.02 × 1026 /kg 19. Two moles of helium gas is mixed with three moles
Radius of Earth : 6.4 × 106 m of hydrogen molecules (taken to be rigid). What is
Gravitational acceleration on Earth = 10 ms–2] the molar specific heat of mixture at constant
volume? [JEE (Main)-2019]
[JEE (Main)-2019]
(R = 8.3 J/mol K)
(1) 104 K (2) 650 K
(1) 19.7 J/mol K (2) 21.6 J/mol K
(3) 800 K (4) 3 × 105 K
(3) 15.7 J/mol K (4) 17.4 J/mol K
14. For a given gas at 1 atm pressure, rms speed of
the molecules is 200 m/s at 127°C. At 2 atm 20. The number density of molecules of a gas depends
pressure and at 227°C, the rms speed of the on their distance r from the origin as,
molecules will be [JEE (Main)-2019] 4
n( r ) n0e – r . Then the total number of molecules
(1) 100 5 m/s (2) 100 m/s is proportional to [JEE (Main)-2019]
(3) 80 5 m/s (4) 80 m/s (1) n0a–3/4 (2) n0 ½
15. An HCl molecule has rotational, translational and (3) n0a1/4 (4) n0a–3
vibrational motions. If the rms velocity of HCI
molecules in its gaseous phase is v , m is its CP 5
21. Two moles of an ideal gas with are mixed
mass and k B is Boltzmann constant, then its CV 3
temperature will be : [JEE (Main)-2019] CP 4
with 3 moles of another ideal gas with C 3 .
V
mv 2 mv 2 CP
(1) (2) The value of for the mixture is
5kB 6kB CV
[JEE (Main)-2020]
mv 2 mv 2 (1) 1.47 (2) 1.42
(3) (4)
7kB 3kB (3) 1.50 (4) 1.45
Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : 011-47623456
Kinetic Theory of Gases
1. One kg of diatomic gas is at a pressure of 5. The mass of a hydrogen molecule is 3.32 × 10–27
8 × 104 N/m2. The density of the gas is 4 kg/m3. kg. If 1023 hydrogen molecules strike, per second,
What is the energy of the gas due to its thermal a fixed wall of area 2 cm2 at an angle of 45° to
motion? [AIEEE-2009] the normal, and rebound elastically with a speed of
(1) 5 × 104 J (2) 6 × 104 J 103 m/s, then the pressure on the wall is nearly
[JEE (Main)-2018]
(3) 7 × 104 J (4) 3 × 104 J
(1) 2.35 × 103 N/m2 (2) 4.70 × 103 N/m2
2. An open glass tube is immersed in mercury in
such a way that a length of 8 cm extends above (3) 2.35 × 102 N/m2 (4) 4.70 × 102 N/m2
the mercury level. The open end of the tube is then 6. A mixture of 2 moles of helium gas (atomic mass
closed and sealed and the tube is raised vertically
= 4 u), and 1 mole of argon gas (atomic mass =
up by additional 46 cm. What will be length of the
40 u) is kept at 300 K in a container. The ratio of
air column above mercury in the tube now?
(Atmospheric pressure = 76 cm of Hg) Vrms (helium)
their rms speeds , is close to
[JEE (Main)-2014] Vrms (argon)
(1) 16 cm (2) 22 cm
[JEE (Main)-2019]
(3) 38 cm (4) 6 cm
(1) 2.24 (2) 0.45
3. Consider an ideal gas confined in an isolated
(3) 3.16 (4) 0.32
closed chamber. As the gas undergoes an
adiabatic expansion, the average time of collision 7. A 15 g mass of nitrogen gas is enclosed in a
between molecules increases as Vq, where V is vessel at a temperature 27°C. Amount of heat
the volume of the gas. The value of q is transferred to the gas, so that rms velocity of
molecules is doubled, is about [JEE (Main)-2019]
CP
[JEE (Main)-2015] [Take R = 83 J/K mole]
Cv
(1) 3 kJ (2) 14 kJ
3 5 3 5 (3) 10 kJ (4) 0.9 kJ
(1) (2)
6 6 8. Two kg of a monoatomic gas is at a pressure of
4 × 104 N/m2. The density of the gas is 8 kg/m3.
1 1 What is the order of energy of the gas due to its
(3) (4)
2 2 thermal motion ? [JEE (Main)-2019]
4. The temperature of an open room of volume 30 m3 (1) 103 J (2) 105 J
increases from 17°C to 27°C due to the sunshine.
The atmospheric pressure in the room remains (3) 104 J (4) 106 J
1 × 10 5 Pa. If n i and n f are the number of 9. A gas mixture consists of 3 moles of oxygen and
molecules in the room before and after heating, 5 moles of argon at temperature T. Considering
then nf – ni will be [JEE (Main)-2017] only translational and rotational modes, the total
(1) –1.61 × 1023 internal energy of the system is
(2) 1.38 × 1023 [JEE (Main)-2019]
(3) 2.5 × 1025 (1) 4 RT (2) 12 RT
(4) –2.5 × 1025 (3) 15 RT (4) 20 RT
Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : 011-47623456
, ARCHIVE - JEE (Main) PHYSICS
10. An ideal gas occupies a volume of 2 m 3 at a 16. The specific heats, CP and CV of a gas of diatomic
pressure of 3 × 106 Pa. The energy of the gas is molecules, A, are given (in units of J mol–1 K–1) by
[JEE (Main)-2019] 29 and 22, respectively. Another gas of diatomic
molecules, B, has the corresponding values 30 and
(1) 108 J (2) 9 × 106 J 21. If they are treated as ideal gases, then
(3) 6 × 104 J (4) 3 × 102 J
[JEE (Main)-2019]
11. An ideal gas is enclosed in a cylinder at pressure
(1) A is rigid but B has a vibrational mode
of 2 atm and temperature, 300 K. The mean time
between two successive collisions is 6 × 10–8 s. (2) A has a vibrational mode but B has none
If the pressure is doubled and temperature is (3) Both A and B have a vibrational mode each
increased to 500 K, the mean time between two
(4) A has one vibrational mode and B has two
successive collisions will be close to
17. A 25 × 10 –3 m 3 volume cylinder is filled with
[JEE (Main)-2019]
1 mol of O2 gas at room temperature (300 K). The
(1) 2 × 10–7 s (2) 3 × 10–6 s molecular diameter of O2, and its root mean square
(3) 0.5 × 10–8 s (4) 4 × 10–8 s speed, are found to be 0.3 nm and 200 m/s,
respectively. What is the average collision rate (per
12. If 10 22 gas molecules each of mass 10 –26 kg
second) for an O2 molecule? [JEE (Main)-2019]
collide with a surface (perpendicular to it)
elastically per second over an area 1 m2 with a (1) ~1012 (2) ~1010
speed 104 m/s, the pressure exerted by the gas (3) ~1011 (4) ~1013
molecules will be [JEE (Main)-2019]
18. A cylinder with fixed capacity of 67.2 lit contains
(1) 1 N/m2 (2) 2 N/m2 helium gas at STP. The amount of heat needed to
(3) 3 N/m2 (4) 4 N/m2 raise the temperature of the gas by 20°C is :
13. The temperature, at which the root mean square [Given that R = 8.31 J mol–1K–1]
velocity of hydrogen molecules equals their escape [JEE (Main)-2019]
velocity from the earth, is closest to (1) 700 J (2) 350 J
[Boltzmann constant kB = 1.38 × 10–23 J/K (3) 374 J (4) 748 J
Avogadro Number NA = 6.02 × 1026 /kg 19. Two moles of helium gas is mixed with three moles
Radius of Earth : 6.4 × 106 m of hydrogen molecules (taken to be rigid). What is
Gravitational acceleration on Earth = 10 ms–2] the molar specific heat of mixture at constant
volume? [JEE (Main)-2019]
[JEE (Main)-2019]
(R = 8.3 J/mol K)
(1) 104 K (2) 650 K
(1) 19.7 J/mol K (2) 21.6 J/mol K
(3) 800 K (4) 3 × 105 K
(3) 15.7 J/mol K (4) 17.4 J/mol K
14. For a given gas at 1 atm pressure, rms speed of
the molecules is 200 m/s at 127°C. At 2 atm 20. The number density of molecules of a gas depends
pressure and at 227°C, the rms speed of the on their distance r from the origin as,
molecules will be [JEE (Main)-2019] 4
n( r ) n0e – r . Then the total number of molecules
(1) 100 5 m/s (2) 100 m/s is proportional to [JEE (Main)-2019]
(3) 80 5 m/s (4) 80 m/s (1) n0a–3/4 (2) n0 ½
15. An HCl molecule has rotational, translational and (3) n0a1/4 (4) n0a–3
vibrational motions. If the rms velocity of HCI
molecules in its gaseous phase is v , m is its CP 5
21. Two moles of an ideal gas with are mixed
mass and k B is Boltzmann constant, then its CV 3
temperature will be : [JEE (Main)-2019] CP 4
with 3 moles of another ideal gas with C 3 .
V
mv 2 mv 2 CP
(1) (2) The value of for the mixture is
5kB 6kB CV
[JEE (Main)-2020]
mv 2 mv 2 (1) 1.47 (2) 1.42
(3) (4)
7kB 3kB (3) 1.50 (4) 1.45
Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : 011-47623456
