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

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What is the average kinetic energy of molecules of an ideal gas leaking freely through an orifice of a container which has $N$ molecules at pressure $P$ in volume $V$ ?

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Important Questions on Kinetic Theory of Gases

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

Which of the following curves represent the variation of coefficient of volume expansion of an ideal gas at constant pressure?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

If the water is converted into ice, and its entropy is changed by

Δ S,

then

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

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 -

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

A mixture of hydrogen and oxygen has volume

500 {cm}^{3},

temperature

300 K,

pressure

400 k Pa

and mass

0.76 g .

The ratio of masses of oxygen to hydrogen will be:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

An ideal gas equation can be written as,

P = \frac{ρ R T}{M_{0}}

where

ρ

and

M_{0}

are respectively,

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

According to the assumptions made in the kinetic theory of gases, when two molecules of a gas collide with each other then

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

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:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

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 of Gases>Kinetic Theory of Gases

Some smoke is trapped in a small glass container and is viewed through a microscope. A number of very small smoke particles are seen in continuous random motion as a result of their bombardment by air molecules. If the mass of the smoke particle is about $10^{12}$ times higher than that of an air molecule the average speed of a smoke particle is

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

Particle

A

of mass

m_{A} = \frac{m}{2}

moving along the

x

-axis with velocity

v_{0}

collides elastically with another particle

B

at rest having mass

m_{B} = \frac{m}{3}

. If both the particles move along the

x

-axis after the collision, the change

∆ λ

in the wavelength of the particle

A

, in terms of its de-Broglie wavelength

(λ_{0})

before the collision is:

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory of Gases

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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What is the average kinetic energy of molecules of an ideal gas leaking freely through an orifice of a container which has N molecules at pressure P in volume V?

Important Questions on Kinetic Theory of Gases

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What is the average kinetic energy of molecules of an ideal gas leaking freely through an orifice of a container which has $N$ molecules at pressure $P$ in volume $V$ ?