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A liquid is in equilibrium with its vapours at its boiling point. On the average, the molecules in the two phases have equal:

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Important Questions on Kinetic Theory

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

H C l

molecule has rotational, translational and vibrational motions. If the rms velocity of

H C l

molecules in its gaseous phase is

\bar{ν}

, m is its mass and

k_{B}

is Boltzmann's constant, then its temperature will be:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The number density of molecules of a gas depends on their distance r from the origin as,

n (r) = n_{0} e^{- α r^{4}} .

Then the numer of molecules is proportional to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

For given gas at

1 a t m

pressure,

r m s

speed of the molecules is

200 m / s

127 ° C .

2 a t m

pressure and at

227 ° C,

the

r m s

speed of the molecules will be:

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

A spring - block system is resting on a frictionless floor as shown in the figure. The spring constant is

2.0 N m^{- 1}

and the mass of the block is

2 .0 kg

. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass

1.0 kg

moving with a speed of

2 .0 m s^{- 1}

collides elastically with the first block. The collision is such that the

2.0 kg

block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.

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EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The molecules of a given mass of gas have RMS velocity of

200

m s^{- 1}

27^{o} C

and

1.0 \times 10^{5} N m^{- 2}

pressure. When the temperature and pressure of the gas are respectively,

127^{o} C

and

0.05 \times 10^{5} N m^{- 2}

, the r.m.s. velocity of its molecules in

m s^{- 1}

is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The RMS speed of oxygen at room temperature is about

500 m s^{- 1}

. The RMS speed of hydrogen at the same temperature is about

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

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 weights of

A

and

B

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

Equal volumes of hydrogen and oxygen gasses of atomic weights

1

and

16

respectively are found to exert equal pressure on the walls of two separate containers. The rms velocities of the two gasses are in the ratio

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

Increase in temperature of a gas filled in a container will lead to

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

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

volume cylinder is filled with

1

mol of

O_{2}

gas at room temperature

(300 K)

. The molecular diameter of

O_{2}

, and its root mean square speed, are found to be

0.3 n m

and

200 m s^{- 1}

, respectively. What is the average collision rate (per second) for an

O_{2}

molecule?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

To raise the temperature of a certain mass of gas by

50 ° C

at a constant pressure,

160

calories of heat is required. When the same mass of gas is cooled by

100 ° C

at constant volume,

240

calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

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

v^{2}

and the mean square rectangular component of the velocity of

A

type is denoted by

ω^{2}

. Then the value of

ω^{2} / v^{2}

is -

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

In a dilute gas at pressure

P

and temperature '

t

', the time between successive collision of a molecule varies with

T

as :

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The root mean square speed of smoke particles each of mass

5 \times 10^{- 17} k g

in their Brownian motion in air at

N . T . P

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

Number of molecules in a volume of

4 {cm}^{3}

of a perfect monoatomic gas at some temperature

T

and at a pressure of

2 cm

of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is

4 \times 10^{- 14} erg, g = 980 cm s^{- 2}

density of mercury

= 13.6 g {cm}^{- 3}

)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The molecules of a monoatomic gas has r.m.s. speed

v

27 ° C

. It is heated until the r.m.s. speed becomes

2 v

. What is the new temperature?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

At what temperature is the $R . M . S .$ velocity of Hydrogen molecule is equal to that of an oxygen molecule at $47 ° C$ ?

(Molecular weight of hydrogen $= 2,$ Molecular weight of oxygen $= 32$ )

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

A mixture of 2 moles of helium gas (atomic mass = 4u)

,

and 1 mole of argon gas (atomic mass = 40 u) is kept at

300 K

in a container. The ratio of their rms speeds

[\frac{V_{r m s} (h e l i u m)}{V_{r m s} (a r g o n)}],

is close to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

Which of the following shows the correct relationship between the pressure

' P'

and density

ρ

of an ideal gas at constant temperature ?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Kinetic Theory of an Ideal Gas

The temperature of an ideal gas is increased from

100 K

400 K

. If the

r m s

speed of the gas molecule is

V

100 K

, then at

400 K

it becomes

A liquid is in equilibrium with its vapours at its boiling point. On the average, the molecules in the two phases have equal:

Important Questions on Kinetic Theory

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