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11th Physics Monthly Test - 1 ( Kinetic Theory of Gases )

MABS Institution

11th Physics Monthly Test - 1 ( Kinetic Theory of Gases )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

A sample of gas consists of \(\mu\)₁ moles of monoatomic molecules, \(\mu\)₂ moles of diatomic molecules and \(\mu\)₃ moles of linear triatomic molecules. The gas is kept at high temperature. What is the total number of degrees of freedom?

[3\(\mu\)₁ + 7( \(\mu\)₂ + \(\mu\)₃)] N_A
[3\(\mu\)₁ + 7\(\mu\)₂ + 6\(\mu\)₃] N_A
[7\(\mu\)₁ + 3( \(\mu\)₂ + \(\mu\)₃)] N_A
[3\(\mu\)₁ + 6( \(\mu\)₂ + \(\mu\)₃)] N_A

The temperature of an ideal gas is increased from 27°C to 927°C. The root mean square speed of its molecules becomes.

3 times
double
4 times
6 times

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature the ratio \(\frac { { C }_{ p } }{ { C }_{ v } } \)for the gas is

\(\frac{4}{3}\)
2
\(\frac{5}{3}\)
\(\frac{3}{2}\)

Two different ideal gases are enclosed in two different vessels at the same pressure. If \(\rho\)₁ and \(\rho\)₂ are their densities and v₁ and v₂ their rrns speeds, respectively then - is equal to ________.

\(\frac { { \rho }_{ 1 }^{ 2 } }{ { \rho }_{ 2 }^{ 2 } } \\ \)
\(\frac { { \rho }_{ 2 }^{ 2 } }{ { \rho }_{ 1}^{ 2 } } \\ \)
\(\sqrt { \frac { { \rho }_{ 1 }^{ } }{ { \rho }_{ 2 }^{ } } }\)
\(\sqrt { \frac { { \rho }_{ 2 }^{ } }{ { \rho }_{ 1 }^{ } } }\)

The speeds of 5 molecules of a gas (in arbitrary units) are as follows: 2, 3, 4, 5, 6 The root mean square speed for these molecule is

2.91
3.52
4.00
4.24

The gas having average molecular speed four times that of SO₂ (molecular mass 64) is

He (molecular mass 4)
O₂ (molecular mass 32)
H₂ (molecular mass 2)
CH₄ (molecular mass 16)

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

Pressure exerted by a perfect gas is equal to

mean K.E. per unit volume
half of mean K.E. per unit volume
one-third of mean K.E. per unit volume
two-third of mean K.E. per unit volume.

The slope at any point on the curve in PV graph for a gas is gn involving the reaction

\(\frac { dp }{ p } =\frac { dV }{ V } \)
\(\frac { dp }{ V } =-\frac { dV }{ P } \)
\(\frac { dp }{ p } =\frac { dV }{ V } \)
\(\frac { dp }{ V } =\frac { dV }{ P } \)

The mean translational K.E. of a perfect gas molecule at absolute temperature T is (K is Boltzmann constant)

\(\frac{1}{2}\)kT
kT
\(\frac{3}{2}\)kT
\(\frac{5}{2}\)kT

Part - B

Generic 2 - Answer All Question

At what temperature does all molecular motion cease? Explain all molecule motion ceases at absolute zero or at 0 K.

What is an ideal gas? (or) What is perfect gas?

The rms velocity of the molecules in a sample of helium is 5/7 times that of molecules in a sample of hydrogen. If the temperature of hydrogen is 0^o. Then, what is the temperature of helium?

What is meant by rms speed of the molecules of a gas? Is rms speed same as the average speed?
What type of motion is associated with the molecule of a gas?

Estimate the total number of air molecules in a room of capacity 25 m³ at a temperature of 27°C.

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).

On which factors does the average K.E. of gas molecules depend?

What are the factors which effect Brownian motion?

When do the real gases obey more correctly the gas equation: PV = nRT?

Part - C

Generic 3 - Answer All Question

State and explain Boyle's law.

What is an ideal gas? Why do the real gases show deviations from ideal behaviour?

At what temperature the rms speed of oxygen atom equal to rms speed of helium gas atom at-10°C?
Atomic mass of helium = 4
Atomic mass of oxygen = 32

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

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

In the upper part of the atmosphere the kinectic temperature of air is of the order of 1000 K, even then one feels severe cold there. Why?

On which factors does the mean free path depend?

Give the kinetic interpretation of temperature.

Write down the postulates of kinetic theory of gases.

Part - D

Generic 5 - Answer All Question

An air bubble of volume 1.0 cm² rises from the bottom of a lake 40 m deep at a temperature of 12°C. To what volume does it grow when it reaches the surface which is at a temperature of 35°C?

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.

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]

Obtain the relation between the pressure and average kinetic energy.

Motor volume is occupied 1 mole of any (ideal) gas at standard temperature and pressure. Show that it is 22.4 litres.

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.
Explain the pressure exerted in a gas column.

Derive Meyer's relation.

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. What is the molecules specific heat of the mixture at constant volume? [8.311moI^-1K^-1]

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.

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