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A vessel contains $1$ mole $O_{2}$ gas at a temperature $T$ . An identical vessel contains one mole of He gas at a temperature $2 T$ . Find the ratio of their pressure ( $He$ to $O_{2}$ ).

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Important Questions on Kinetic Theory of Gases

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 13

Given figure shows a horizontal cylindrical container of length

30 c m

, which is partitioned by a tight-fitting separator. The separator is diathermic but conducts heat very slowly. Initially the separator is in the state shown in the figure. The temperature of left part of cylinder is

100 K

and that on right part is

400 K

. Initially the separator is in equilibrium. As heat is conducted from right to left part, separator displaces to the right. Find the displacement of separator (in

cm

) after a long time when gases on the two parts of cylinder are in thermal equilibrium.
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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 1

One kilogram of a diatomic gas is at a pressure of

8 \times 10^{4} N m^{- 2}

. The density of the gas is

4 kg m^{- 3}

. What is the energy of the gas due to its thermal motion?

HARD

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 3

Consider a spherical shell of radius

R

at a temperature

T

. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u = \frac{U}{V} \propto T^{4}

and pressure

p = \frac{1}{3} (\frac{U}{V})

. If the shell now undergoes an adiabatic expansion the relation between

T

and

R

is :

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 1

A real gas behaves like an ideal gas if its

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 2

A mixture of

2

moles of helium gas (atomic mass

= 4 amu

) and

1

mole of argon gas (atomic mass

= 40 amu

) is kept at

300 K

in a container. The ratio of the rms speed

(\frac{v_{rms} (helium)}{v_{rms} (argon)})

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 4

A vessel contains a mixture of

1

mole of oxygen and 2 moles of nitrogen at

300 K

. Find the ratio of average rotational kinetic energies per

O_{2}

molecule to per

N_{2}

molecule.

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 9

A vessel of volume

33.2 \times 10^{- 3} m^{3}

contains an ideal gas at

300 K

and

200 kPa

. The gas is allowed to leak till the pressure falls to

125 kPa

. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant? (Given

R = 8.3 J / mol - K

)

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 15

Oxygen is filled in a closed metal jar of volume

1.0 \times 10^{- 3} m^{3}

at a pressure of

1.5 \times 10^{5} Pa

and temperature

400 K

. The jar has a small leak in it. The atmospheric pressure is

1.0 \times 10^{5} Pa

and the atmospheric temperature is

300 K

. Find the mass (in

g

) of the gas that leaks out by the time the pressure and the temperature inside the jar equalise with the surrounding.

A vessel contains 1 mole O2 gas at a temperature T. An identical vessel contains one mole of He gas at a temperature 2T. Find the ratio of their pressure (He to O2).

Important Questions on Kinetic Theory of Gases

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A vessel contains $1$ mole $O_{2}$ gas at a temperature $T$ . An identical vessel contains one mole of He gas at a temperature $2 T$ . Find the ratio of their pressure ( $He$ to $O_{2}$ ).