Kinetic Theory of Gases Exercises - JEE Main by ednexa.com

1. Kinetic theory of gases and radiation
Exercise
1. What is an ideal gas or perfect gas? State equation of an ideal gas.
Sol: An ideal gas or perfect gas is defined to be a gas which obeys the gas laws at all
pressure and temperatures.
The equation of an ideal gas is given below:
A gas molecule may be treated as an ideal particle, having only two attributes,
mass and velocity. Its structure and size are ignored.
Intermolecular forces are zero except during collinear.
The microscopic thermodynamic variables, namely, the amount of gas (in mole),
the pressure p, the volume V and the thermodynamic (Or absolute) temperature
T, are related by the equation, pV = nRT
Where n ≡ number of moles and R is the molar gas constant. This is the
equation state of an ideal gas and describe the microscopic behavior of an ideal
gas under all possible conditions.
2. State the basic assumptions of the kinetic theory of gases.
Sol: - The basic assumptions of the kinetic theory of an ideal gas are as follows:
a. A gas of a pure material consists of an extremely large number of identical
molecules.
b. The molecules are in constant random motion with various velocities and
obey
Newton’s laws of motion.
c. A gas molecule can be traded as an ideal particle, i.e. it has mass but its
structure and
size can be ignored as compared with the intermolecular separation in a
dilute gas and
the dimensions of the container.
d. Intermolecular forces may be ignored on the average so that the only
forces between the molecules and the walls of the container are contact
forces during collisions.
e. The collisions are perfectly elastics conserving total momentum and
kinetic energy, and
the duration of the collision is very small compared to the time interval
between successive collisions.

2. f. Between the collisions, a gas molecule travels in a straight line with
constant speed.
3. Deduce Boyle’s law, using the expansion for pressure exerted by a gas.
Sol: At a constant temperature, the pressure exerted by a fixed mass of a gas is
inversely proportional to its volume. If p and V denote the pressure and volume of
a fixed mass of a gas, then pV = constant and volume of fixed mass of a gas.
This is Boyle’s law.
According to the kinetic theory of an ideal gas, the pressure by the gas is given
by
2
0 rmsNm c1
p
3 V

Where N is the number of molecules of the gas, m0 is the mass of single
molecules, rmsc is the r.m.s speed of the molecules and V is the volume occupied
by the gas.
We can write the above equation as
   
2
0 rms
1 2
pV m c N
2 3
2
KE of a gas molecules N ......... 1
3
    
 
For a fixed mass of a gas, N is constant. Further, in the ideal-gas model,
intermolecular forces are ignored so that the potential energy of the gas
molecules may be assumed to be zero. Therefore, 2
0 r ms
1
m c
2
is also the total
energy of a gas molecule and 2
0 rms
1
N m c
2
    
is the total energy of the gas
molecules, which is proportional to the absolute temperature of the gas,
then, the right-hand side of equation (1) will be is constant. Hence, it follows that
pv = constant for an isolated mass of gas at constant temperature.
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