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11th Physics Monthly Test - 2 ( Kinetic Theory of Gases )

MABS Institution

11th Physics Monthly Test - 2 ( Kinetic Theory of Gases )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If the temperature and pressure of a gas is doubled the mean free path of the gas molecules

remains same
doubled
tripled
quadrapoled

Oxygen and hydrogen gases are at the same temperature the ratio of the average K.E of an oxygen molecule and that of a hydrogen molecule is

16
4
1
\(\frac{1}{4}\)

Two vessels have equal volumes. One of them contains hydrogen at one atmosphere and the other helium at two atmospheres. If both the samples are at the same temperature, the rms velocity of the hydrogen molecules is _________.

equal to that of the helium molecules
twice that of the helium molecules
half that of the helium molecules
\(\sqrt 2\) times that of the helium molecules

Two gases are enclosed in a container at constant temperature. One of the gases, which is diatomic, has relative molecular mass eight times the other, which is monoatomic. The ratio of the rms speed of the molecules of the monoatomic gas to that of the molecules of the diatomic gas is ________

8
4
2\(\sqrt2\)
2

Two identically sized rooms A and B are connected by an open door. If the room A is air conditioned such that its temperature is 4°C lesser than room B, which room has more air in it?

Room A
Room B
Both room has same air
Cannot be determined

The temperature of a gas is raised from 27°C to 927°C. The root mean square speed of its molecules _______.

becomes \(\sqrt \frac{927}{27}\) times the earlier value
gets halved
remains the same.
gets doubled

The kinetic theory of gases breaks down most at _________.

low pressure and high temperature
high pressure and low temperature
low pressure and low temperature
high pressure and high temperature

The average K.E of a molecule.

is inversely proportional to the molecular mass of the gas.
is inversely proportional to the absolute temperature mass of the gas.
is directly proportional to the absolute temperature mass of the gas.
is not dependent on absolute temperature of the gas.

For hydrogen gas C_P- C_V= A and for oxygen gas C_P- C_V= B, so the relation between A and B is given by

A = 16B
16A=B
A = 4B
A = B

Four molecules have speed 2 km/s, 3 km/s, 4 km/s and 5 km/s. The rms speed of these molecules in km/s is ________

\(\sqrt\frac{27}{2}\)
\(\sqrt{27}\)
2\(\sqrt{27}\)
\(\sqrt{54}\)

Part - B

Generic 2 - Answer All Question

State Avogadro's law.

A fresh air is composed of nitrogen N₂(78%) and oxygen O₂(21%). Find the rms speed of N₂ and O₂ at 20°C.

Deduce Avogadro’s law based on kinetic theory.

On reducing the volume of a gas at constant temperature, the pressure of the gas increases. Explain it on the basis of kinectic theory.

Calculate the mean free path of air molecules at STP. The diameter of N₂ and O₂ is about 3 × 10_-10 m

What is the microscopic origin of temperature?

From kinetic theory of gases, show that Moon cannot have an atmosphere (Assume k = 1.38 × 10^-23 J K^-1 Temperature T=0°C=273K).

Part - C

Generic 3 - Answer All Question

Derive the ratio of two specific heat capacities of monoatomic, diatomic and triatomic molecules.

Derive the expression of pressure exerted by the gas on the walls of the container.

Explain in detail the kinetic interpretation of temperature.

On which factors does the mean free path depend?

Derive an expansions for the work done in one cycle during adiabetre expansion.

Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.

Estimate the total number of molecules inclusive of oxygen, nitrogen, water vapour and other consituents in a room of capacity 30 m³ at a temperature of 30°C and 1 atmosphere pressure.

Part - D

Generic 5 - Answer All Question

Speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20°C? [Atomic mass of Ar =39.90, He =4.04]

0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27°C. How much heat has to be 'transferred to double the rms speed of its molecules.

An oxygen molecule is travelling in air at 300 K and 1 atm, and the diameter of oxygen molecule is 1.2 × 10⁻¹⁰m. Calculate the mean free path of oxygen molecule.

A room contains oxygen and hydrogen molecules in the ratio 3:1. Th e temperature of the room is 27°C. The molar mass of 02 is 32 g mol-1 and for H₂ 2 g mol^-1. The value of gas constant R is 8.32 J mol^-1 K^-1.
Calculate
(a) rms speed of oxygen and hydrogen molecule
(b) Average kinetic energy per oxygen molecule and per hydrogen molecule
(c) Ratio of average kinetic energy of oxygen molecules and hydrogen molecules.

Calculate the rms speed, average speed and the most probable speed of 1 mole of hydrogen molecules at 300 K. Neglect the mass of electron.
Motor volume is occupied 1 mole of any (ideal) gas at standard temperature and pressure. Show that it is 22.4 litres.

Explain postulates of the kinetic theory of gases.

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