EASY

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The rms speed of a gas molecule is

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Important Questions on Kinetic Theory

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

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

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

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

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

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

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

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:

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

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 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

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 temperature at which the r.m.s. velocity of oxygen molecules will be

{(\frac{1}{3})}^{rd}

r \cdot m . s

velocity of hydrogen molecules at

- 3 ° C

EASY

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

Consider a sample of oxygen behaving like an ideal gas. At $300 K$ , the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :

(Molecular weight of oxygen is $32 g {mol}^{- 1}; R = 8.3 J K^{- 1} {mol}^{- 1}$ )

EASY

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

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

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

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

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 -

The rms speed of a gas molecule is

Important Questions on Kinetic Theory

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