HARD

Earn 100

A cubical box of side 1m contains helium gas ( atomic weight 4 ) at a pressure of 100 N/m². During an observation time of 1 s, an atom travelling with the root mean square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. Take, $R = \frac{25}{3} J/mol-K and k = 1 \cdot 38 \times 1 0^{- 23} J/K.$

(a) Evaluate the temperature of the gas.
(b) Evaluate the average kinetic energy per atom.
(c) Evaluate the total mass of helium gas in the box.

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Important Questions on Kinetic Theory of Gases

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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>Pressure of a 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 of Gases>Pressure of a 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

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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>Pressure of a 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 of Gases>Pressure of a 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 of Gases>Pressure of a 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 of Gases>Pressure of a 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 $32 g {mol}^{- 1}; R = 8.3 J K^{- 1} {mol}^{- 1}$ )

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a 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}]

EASY

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

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a 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 of Gases>Pressure of a 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 of Gases>Pressure of a Gas

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>Pressure of a Gas

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>Pressure of a Gas

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>Pressure of a 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:

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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>Pressure of a Gas

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

)

Important Questions on Kinetic Theory of Gases

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