An ideal gas equation can be written as, P = ρ R T M 0 where ρ and M 0 are respectively,

number density, mass of the gas

EASY

Earn 100

Two closed vessels of equal volume contain air at 105 kPa, 300 K and are connected through a narrow tube. If one of the vessels is now maintained at 300 K and other at 400 K, What will be the pressure in the vessels?

Important Questions on Kinetic Theory of Gases

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

An ideal gas equation can be written as,

P = \frac{ρ R T}{M_{0}}

where

ρ

and

M_{0}

are respectively,

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

One mole of an ideal gas passes through a process where pressure and volume obey the relation

P = P_{o} [1 - \frac{1}{2} {(\frac{V_{o}}{V})}^{2}]

. Here

P_{o}

and

V_{o}

are constants. Calculate the change in the temperature of the gas if its volume changes from

V_{o}

2 V_{o}

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

A cylinder contains hydrogen gas at pressure of

249 kPa

and temperature

27^{o} C

. Its density is:

(R = 8 .3 JK {Mol}^{- 1} K^{- 1})

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Tyre of a bicycle has volume

2 \times 10^{- 3} m^{3}

. Initially the tube is filled

75 %

of its volume by air at atmospheric pressure

10^{5} N m^{- 2}

. When a rider is on the bicycle, the area of contact of tyre with road is

24 \times 10^{- 4} m^{2}

. The mass of rider with bicycle is

120 kg

. If a pump delivers a volume

500 {cm}^{3}

of air in each stroke then the number of strokes required to inflate the tyre is

(g = 10 m s^{- 2})

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

The temperature of an open room of volume

30 m^{3}

increases from

17 ° C

27 ° C

due to the sunshine. The atmospheric pressure in the room remains

1 \times 10^{5} Pa

. If

n_{i}

and

n_{f}

are the number of molecules in the room before and after heating, then

n_{f} - n_{i}

will be:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

If a kilo mole of methane gas weighs

16 kg

, the density of methane at

20 ° C

and

5 atm

pressure is (Use

R = 8314 J k^{- 1} mol - K

)

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

The equation of state for

2 g

of oxygen at a pressure

p

and temperature

T

, when occupying a volume

V

will be

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Two non-reactive monatomic ideal gases have their atomic masses in the ratio

2 : 3

. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature is

4 : 3

. The ratio of their densities is

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

For the

P - V

diagram given for an ideal gas
Question Image

Out of the following which one correctly represents the

T - P

diagram?

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

A container

A B

in the shape of a rectangular parallelepiped of length

5 m

is divided internally by a movable partition

P

as shown in the figure.
Question Image

The left compartment is filled with a given mass of an ideal gas of molar mass

32

while the right compartment is filled with an equal mass of another ideal gas of molar mass

18

at same temperature. What will be the distance of

P

from the left wall

A

when equilibrium is established?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of gas

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

0.02

moles of an ideal diatomic gas with initial temperature

20 ° C

is compressed from

1500 {cm}^{3}

500 {cm}^{3}

. The thermodynamic process is such that

p V^{2} = β

, where

β

is a constant. Then, the value of

β

is close to (the gas constant,

R = 831 J K^{- 1} {mol}^{- 1}

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Two vessels separately contain two ideal gases

A

and

B

at the same temperature. The pressure of gas

A

is three times the pressure of gas

B

. Under these conditions, the density of gas

A

is found to be two times the density of

B

. The ratio of molecular weights of gas

A

and

B

i.e.

\frac{M_{A}}{M_{B}}

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Different curves in the figure show the behaviour of gases

Question Image

(i) Curve I represent ideal gas behaviour
(ii) Curves II, III and IV also represents ideal gas behaviour at different temperatures $T_{2}, T_{3}$ and $T_{4}$
(iii) Curves II, III and IV represents behaviour of a real gas at different temperatures $T_{2}, T_{3}$ and $T_{4}$
(iv) $T_{2} > T_{3} > T_{4}$
(v) $T_{2} < T_{3} < T_{4}$
The correct statements are

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

Two gases having same pressure

P

and volume

V

are mixed at a temperature

T

. If the mixture is at a temperature

T

and occupies the same volume then pressure of the mixture would be

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

For Boyle's law to hold good the necessary condition is

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

An open glass tube is immersed in mercury in such a way that a length of

8 cm

extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional

46 cm

. What will be length of the air column above mercury in the tube now ?
(Atmospheric pressure =

76 cm

of Hg)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

A given sample of an ideal gas occupies a volume,

V

at a pressure,

P

and absolute temperature,

T

. The mass of each molecule of the gas is

m

. Which of the following gives the density of the gas?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Equation of State of a Perfect Gas

A vertical closed cylinder is separated into two parts by a frictionless piston of mass

m

and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is

l_{1},

and that below the piston is

l_{2},

such that

l_{1} > l_{2} .

Each part of the cylinder contains

n

moles of an ideal gas at equal temperature

T .

If the piston is stationary, its mass

m

will be given by:
(

R

is universal gas constant and

g

is the acceleration due to gravity)

Two closed vessels of equal volume contain air at 105 kPa, 300 K and are connected through a narrow tube. If one of the vessels is now maintained at 300 K and other at 400 K, What will be the pressure in the vessels?

Important Questions on Kinetic Theory of Gases

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