BEHAVIOUR OF PERFECT GAS ANS KINETIC THEORY
CONCEPTUAL PROBLEMS
Q-01
Ans
Two different gases have exactly the same temperature. Does this mean that their molecules have the
same r.m.s. speed ?
When the two gases have exactly the same temperature, the average kinetic energy per molecule
for each gas is the same. But as the different gases may have molecules of different
masses, the r.m.s. speed (C) of molecules of different gases shall of different.
Q-02
Ans
Distinguish between average speed and r.m.s. speed. If three molecules have speeds u1 , u2 , u3 what will
be their average speed and r.m.s. speed.
Average speed is the arithmetic mean of the speeds of the molecules.
∴
Average speed =
r.m.s. speed is the root mean square speed and is defined as the square root of the mean of the squares of
different speeds of the individual molecules.
r.m.s. speed =
Q-03
Ans
A gas is filled in a cylinder fitted with a piston at a definite temperature and pressure. Explain on the
basis of kinetic theory, the pressure of the gas increases by raising its temperature.
On raising the temperature, the average velocity of the gas molecules increases. As a result of which
more molecules collide with the wall of the cylinder per second and hence greater momentum is
transferred to the wall per second. Due to both these reasons, the pressure increases.
Q-04
Ans
Q-05
Ans
Q-06
A gas is filled in a cylinder fitted with a piston at a definite temperature and pressure. Explain on the
basis of kinetic theory : on pulling the piston out, the pressure of gas decreases.
On pulling the piston out, the volume of the cylinder for the given gas increases. Due to which the
molecules of gas get more space to move about. As a result of which, less molecules will collide with the
wall of cylinder per second and hence less momentum is transferred to the walls Per second. In addition
to it, now these collisions take place on the large area of the walls. Due to both these reasons, the pressure
decreases.
On reducing the volume of the gas at constant temperature, the pressure of the gas increases. Explain on
kinetic theory.
On reducing the volume, the space for the given number of molecules of the gas decreases i.e. no. of
molecules per unit volume increases. As a result of which more molecules collide with the walls of the
vessel per second and hence a larger momentum is transferred to the walls per second. Due to which the
pressure of the gas increases.
Under what conditions do the real gases obey more strictly the gas equation, PV = RT ? Explain.
1
Ans
The basic properties of the molecules of an ideal gas are (i) zero size of the molecules and hence zero
volume of the molecules and (ii) no mutual intermolecular forces between them. At low pressure, the
volume of the given gas becomes large. Therefore the volume of the molecules becomes negligible in
comparison to the volume of the gas. At high temperature, the molecules have large K.E. and so the effect
of the intermolecular force on the motion of the molecules becomes negligible. Hence at low pressure and
high temperature the real gas behaves as ideal gas and gas equation is obeyed.
Q-07
Ans
Explain the phenomenon of evaporation on the basic of kinetic Theory.
According to kinetic Theory, molecules of a liquid are in a state of continuous random motion. The
molecules near the surface of liquid may have enough kinetic energy so as to overcome the
intermolecular attraction of other molecules on the surface and hence mange to escape. Such molecule
would move around freely in the space above the liquid. This is the phenomenon of evaporation which
may occur at all temperatures.
Q-08
Ans
Why cooling is caused by evaporation ?
As explained in problem 10, evaporation occurs on account of faster molecules escaping from the surface
of the liquid. The liquid is therefore left with molecules having lower speeds. The decrease in the average
speed of the molecules results in lowering the temperature. That is why cooling is caused by evaporation.
Q-09
Two perfect gases at absolute temperatures T1 and T2 are mixed. There is no loss of energy. Find the
temperature of the mixture if the masses of the molecules are m1 and m2 and the number of the molecules
in the gases are n1 and n2 respectively.
Ans
According to kinetic theory, the average K.E. per molecule of a gas =
Before mixing, the two gases, the average K.E. of all the molecules of two gases
After mixing, the average K.E. of both the gases =
Where T is the temperature of mixture. Since there is no loss of energy, hence
or
VERY SHORT ANSWER QUESTIONS
Q-01
Ans
What is the value of gas constant in c.g.s. system for 1 gram of helium ?
2∙078 × 107 erg g−1 0C−1
Q-02
Obtain the dimensional formula for R used in the ideal gas equation PV = RT.
Ans
Q-03
Ans
What is meant by Boltzmann constant ? Calculate its value in SI units.
Boltzmann constant KB = R/N, where R is universal gas constant and NA is the Avogadro’s number.
∙
∙
∙
2
Q-04
Ans
Although the r.m.s. speed of gas molecules is of the order of the speed of sound in that gas, yet on
opening a bottle of ammonia in one corner of a room, its smell takes time in reaching the other corner.
Explain why ?
Because the molecules of ammonia move at random and continuously collide with one another. As a
result of which they are not able to advance in one particular direction speedly.
Q-05
The pressure of a gas at -1730C temperature is 1 atmosphere, keeping the volume constant, to what
temperature should the gas be heated so that its pressure becomes 2 atmosphere.
Ans
P1/T1 = P2/T2 or T2 = P2 T1 /P1 =
Q-06
The ratio of vapour densities of two gases at the same temperature is 8 : 9. Compare the r.m.s. velocities
of their molecules.
= 200 K = −730C
Ans
Q-07
A vessel is filled with a mixture of two different gases. State with reason (i) Will the mean K.E. per
molecule of both the gases be equal ? (ii) Will the root mean square velocities of the molecules be equal
(iii) will the pressures be equal ?
Ans
(i) yes, because the mean K.E. per molecule
depends only upon the temperature.
(ii) No, because for different gases r.m.s. velocity depends upon the mass of the gas molecules.
(iii) No definite idea about pressure because masses of the gases are not given.
Q-08
The velocities of three molecules are 3 , 4 and 5 . Calculate their root-mean-square velocity.
Ans
Q-09
Ans
1 cm3 of hydrogen and 1 cm3 of oxygen are given at N.T.P. Explain with reason, which will have larger
number of molecules.
Both will have equal number of molecules, according to Avogadro’s hypothesis.
Q-10
Ans
What is the correct value of 00C on the Kelvin scale ?
273∙15 K
Q-11
Helium gas is filled in a closed vessel whose coefficient of thermal expansion is negligible. When it is
heated from 300 K to 600 K, then find the average kinetic energy of helium atoms.
The K.E. becomes double, because average K.E. per molecule of a gas is directly proportional to
temperature in Kelvin.
Ans
Q-12
Ans
Oxygen and hydrogen are at the same temperature T. What is the ratio of kinetic energies of oxygen
molecule and hydrogen molecule when oxygen is 16 times heavier than hydrogen ?
One, because the kinetic energy per molecule of the gas depends only upon the temperature.
3
Q-13
The absolute temperature of the gas is increased 3 times. What will be the increase in root mean square
velocity of the gas molecules ?
Ans
C∝
. Therefore, the r.m.s. velocity becomes
increase in r.m.s. velocity =
Q-14
C. Hence
C – C = 0∙732 C.
Ans
In given samples of 1 c.c. of hydrogen and 1 c.c. of oxygen at N.T.P, which sample has larger number of
molecules ?
Both the samples will contain the same number of molecules, in accordance with Avogadro’s law.
Q-15
Ans
Can the temperature of a gas be increased keeping its pressure and volume constant ?
No, temperature cannot be change without changing V or P.
SHORT ANSWER QUESTIONS
Q-01
Explain the rise of temperature on heating, on the basis of kinetic theory.
Ans
When heat is given to a gas, the r.m.s velocity of the gas molecules increases. As C ∝
of the gas increases.
Q-02
Ans
On driving the scooter for a long time, the air pressure in the tyres slightly increases. Why ?
On driving a scooter for a long time, the work done against friction is converted into heat. Due to which
the gas in the tyre gets heated and hence the pressure of the gas increases because P ∝ T.
Q-03
The pressure of a given mass of a gas is halved at constant temperature. What will be the volume of the
gas in comparison to its initial volume. Explain on the basis of kinetic theory.
Ans
As, P =
or V =
i.e. V ∝
(
, so temperature
a constant, when temperature is constant)
Therefore if P becomes P/2, V becomes double.
Q-04
Two gases A and B each at temperature T, pressure P and volume V, are mixed. If the mixture be at the
same temperature T and its volume also be V, then what should be its pressure ? Explain.
Ans
As, P =
, but C2 ∝ T ; therefore if V and T are constants, then P ∝ M. As M becomes 2 M, P becomes
2 P.
Q-05
Two vessels of the same volume are filled with the same gas at the same temperature. If the pressure of
the gas in these vessels be in the ratio 1 : 2, then state : (i) the ratio of the r.m.s. speeds of the molecules,
(ii) the ratio of the number of molecules.
Ans
As, P =
so P ∝
when
and V are constants. But C ∝
As the temperature of two vessels is
the same, the r.m.s. velocity of gas molecules in two vessels will be the same. When temperature is same
for two vessels then P ∝ . i.e.
Q-06
The volume of vessel A is twice the volume of another vessel B and both of them are filled with the same
gas. If the gas in A is at twice the temperature and twice the pressure in comparison to the gas in B, what
is the ratio of gas molecules in A and B ?
4
Ans
Here,
and
∴
Q-07
Ans
On which of the following factors does the average kinetic energy of gas molecules depend ? (i) Nature of
the gas, (ii) absolute temperature, (iii) volume. What will be its value at the absolute zero ?
The average kinetic energy of gas molecules (i) is independent of the nature of the gas
(ii) depends upon the temperature of the gas as
∝
(iii) is independent of the volume of the gas.
At absolute zero, r.m.s velocity of the gas molecules become zero so mean K.E. per molecule of the gas
becomes zero at absolute zero.
Q-08
A gas in a vessel is at the pressure P0. If the masses of all the molecules be made half and their speeds be
made double, then find the resultant pressure.
Ans
P0 =
Q-09
Under what conditions of pressure and temperature, a gas can be assumed as an ideal gas ? Explain.
Q-10
Explain the concept of absolute zero of temperature on the basis of kinetic theory of gases.
Q-11
What is an ideal gas ? Explain its main characteristics.
Q-12
The pressure of a gas increases on increase of its temperature and also on decrease of its volume. How
are two cases different on the basic of kinetic theory of gases ?
Q-13
State law of equipartition of energy. Use this law of equipartition to calculate specific heats of
monoatomic, diatomic and triatomic gases.
Q-14
Obtain the relation between degrees of freedom of a gas and ratio of two principal specific heats of the
gas.
and
LONG ANSWER QUESTIONS
Q-01
Explain (i) Boyle’s law (ii) Charle’s law. Why they are not applicable to real gases at all states ?
Q-02
State and explain (i) Gay lussac’s law and (ii) Gas equation. Distinguish clearly between R and r for a gas.
Q-03
State the postulates of kinetic Theory of gases. Explain the pressure exerted by an ideal gas.
Q-04
Find an expression for the pressure exerted by a gas and establish its relation with kinetic energy of the
gas.
Q-05
From Kinetic Theory of gases, explain kinetic interpretation of temperature and absolute zero.
5
Q-06
From Kinetic Theory of gases, explain the various gas laws.
Q-07
Explain the meaning of mean speed, rms speed and most probable speed.
Q-08
What is meant by degrees of freedom ? State law of equipartition of energy. Hence calculate specific
heats of mono, di and triatomic gases.
Q-09
Explain the concept of mean free path.
Q-10
Explain what is meant by Brownian Motion ?
6