EASY

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The temperature of an ideal gas is increased from $200 K$ to $800 K$ . If r.m.s. speed of gas at $200 K$ is $v_{0}$ . Then, r.m.s. speed of the gas at $800 K$ will be:

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Important Questions on Kinetic Theory

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

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

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

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

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

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

Which of the following shows the correct relationship between the pressure

' P'

and density

ρ

of an ideal gas at constant temperature ?

MEDIUM

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

Two gases - argon (atomic radius

0.07 n m,

atomic weight

40

) and xenon (atomic radius

0.1 n m,

atomic weight

140

) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:

MEDIUM

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

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on

T a s T^{q}

. A good estimate for q is:

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

MEDIUM

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

10^{22}

gas molecules each of mass

10^{- 26}

kg collides with a surface (perpendicular to it) elastically per second over an area

1 m^{2}

with a speed

10^{4} m / s,

the pressure exerted by the gas molecules will be of the order of:

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:

MEDIUM

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

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to:

[

Boltzmann Constant

k_{B} = 1.38 \times 10^{- 23} J / K

Avogadro number

N_{A} = 6.02 \times 10^{26} / k g

Radius of Earth:

6.4 \times 10^{6} m

Gravitational acceleration on Earth

= 10 m s^{- 2}]

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

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 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

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>Kinetic Theory of an Ideal Gas

15 g

mass of nitrogen gas is enclosed in a vessel at a temperature,

27^{o} C

. The amount of heat transferred to the gas, so that

R . M . S .

velocity of molecules is doubled, is about.

[R = 8 .3 J {(K mole)}^{- 1}]

MEDIUM

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

At what temperature will the rms speed of oxygen molecules becomes just sufficient for escaping from the Earth's atmosphere? (Given Mass of oxygen molecules

m = 2.76 \times 10^{- 26} kg

, Boltzmann's constant

k_{B} = 1.38 \times 10^{- 23} J K^{- 1}

)

The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is v0. Then, r.m.s. speed of the gas at 800 K will be:

Important Questions on Kinetic Theory

Learn and Prepare for any exam you want !

The temperature of an ideal gas is increased from $200 K$ to $800 K$ . If r.m.s. speed of gas at $200 K$ is $v_{0}$ . Then, r.m.s. speed of the gas at $800 K$ will be: