HARD

Earn 100

Find the modulus of the mean velocity vector averaged over the first $t \sec$ of motion.

Important Questions on Kinetic Theory of Gases and Radiation

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

Nitrogen gas is at

300 ° C

temperature. The temperature (in

K

) at which the rms speed of a

H_{2}

molecule would be equal to the rms speed of a nitrogen molecule, is

\dots \dots \dots .

(Molar mass of

N_{2}

gas

28 g

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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 and Radiation>Mean Free Path

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

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

The

rms

speed of a particle is

v_{rms}

at a pressure

P .

If pressure is increased to

3

times then the rms speed becomes

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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 of Gases and Radiation>Mean Free Path

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 of Gases and Radiation>Mean Free Path

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 and Radiation>Mean Free Path

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 $32 g {mol}^{- 1}; R = 8.3 J K^{- 1} {mol}^{- 1}$ )

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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}]

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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 and Radiation>Mean Free Path

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 of Gases and Radiation>Mean Free Path

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

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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 of Gases and Radiation>Mean Free Path

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 of Gases and Radiation>Mean Free Path

The root-mean-square speed of molecules of a given mass of a gas at

27 ° C

and

1

atmosphere pressure is

200 m s^{- 1} .

The root-mean-square speed of molecules of the gas at

127 ° C

and

2

atmosphere pressure is

\frac{x}{\sqrt{3}} m s^{- 1} .

The value of

x

will be __________.

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

The absolute temperature of a gas is increased to 16 times of the original temperature. The rms speed of its molecules will become

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

Consider a mixture of gas molecule of types

A, B

and

C

having masses

m_{A} < m_{B} < m_{C} .

The ratio of their root mean square speeds at normal temperature and pressure is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

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:

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature

T

. Assuming the gases are ideal, the correct statement(s) is (are)

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases and Radiation>Mean Free Path

The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at

20 ° C

and

1

atmospheric pressure is of the order of (

k_{b} = 1.4 \times 10^{- 23} J K^{- 1}

and the average mass of an air molecule is

5 \times 10^{- 27} kg

)

Find the modulus of the mean velocity vector averaged over the firstt sec of motion.

Important Questions on Kinetic Theory of Gases and Radiation

Learn and Prepare for any exam you want !

Find the modulus of the mean velocity vector averaged over the first $t \sec$ of motion.