CBSE Class 11 Physics Chapter 13 Kinetic Theory Study Materials

1 Marks Questions

1.Given Samples of 1 cm³ of Hydrogen and 1 cm³ of oxygen, both at N. T. P. which sample has a larger number of molecules?

Ans.Acc. to Avogadro’s hypothesis, equal volumes of all gases under similar conditions of temperature and pressure contain the same number of molecules. Hence both samples have equal number of molecules. Hence both samples have equal number of molecules.

2.Find out the ratio between most probable velocity, average velocity and root Mean square Velocity of gas molecules?

Ans.Since,

Most Probable velocity,  

Average velocity,  

Root Mean Square velocity: Vr.m.s.  

So, 

3.What is Mean free path?

Ans.Mean free path is defined as the average distance a molecule travels between collisions. It is represented by. Units are meters (m).

4.What happens when an electric fan is switched on in a closed room?

Ans.When electric fan is switched on, first electrical energy is converted into mechanical energy and then mechanical energy is converted into heat. The heat energy will increase the Kinetic energy of air molecules; hence temperature of room will increase.

5.State the law of equi-partition of energy?

Ans.According to law of equi partition of energy, the average kinetic energy of a molecule in each degree of freedom is same and is equal to 

6.On what factors, does the average kinetic energy of gas molecules depend?

Ans.Average kinetic energy depends only upon the absolute temperature and is directly proportional to it.

7.Why the temperature less than absolute zero is not possible?

Ans.Since, mean square velocity is directly proportional to temperature. If temperature is zero then mean square velocity is zero and since K. E. of molecules cannot be negative and hence temperature less than absolute zone is not possible.

8.What is the relation between pressure and kinetic energy of gas?

Ans.Let, Pressure = P

Kinetic energy = E

From, Kinetic theory of gases,  

S = Density

C = r.m.s velocity of gas molecules

Mean Kinetic energy of translation per unit

Volume of the gas = 

Dividing  1) by 2)

9.What is an ideal perfect gas?

Ans.A gas which obeys the following laws or characteristics is called as ideal gas.

1) The size of the molecule of gas is zero

2) There is no force of attraction or repulsion amongst the molecules of gas.

Very Short Answer Type Question (1 Marks)

1. Write two condition when real gases obey the ideal gas equation (PW = nRT). N → number of mole.
   Ans. (i) Low pressure (ii) High temperature
2. In the number of molecule in a container is doubled. What will be the effect on the rms speed of the molecules?
   Ans. No effect
3. Draw the graph between P and 1/W (reciprocal of volume) for a prefect gas at constant temperature.
   Ans.
   
   
4. Name the factors on which the degree of freedom of gas depends.
   Ans. Atomicity and temperature
5. What is the volume of a gas at absolute zero of temperature?
   Ans. 0
6. How much volume does one mole of a gas occupy at NTP?
   Ans. 22.4 litre
7. What is an ideal gas?
   Ans. Gas in which intermolecular forces are absent
8. The absolute temperature of a gas is increased 3 times what is the effect on the root mean square velocity of the molecules?
   Ans. increases 
9. What is the Kinetic Energy per unit volume of a gas whose pressure is P.
   Ans. 3P/2
10. A container has equal number of molecules of hydrogen and carbon dioxide, If a fine hole is made in the container, then which of the two gases shall leak out rapidly?
11. What is the mean translational Kinetic energy of a perfect gas molecule at temperature T?
    Ans. Hydrogen (rms speed is greater)
12. Why it is not possible to increase the temperature of a gas while keeping its Volume and pressure constant.
    Ans. 
    P and V are constant then T is also constant.

2 Marks Questions

1.If a certain mass of gas is heated first in a small vessel of volume V₁ and then in a large vessel of volume V₂. Draw the P – T graph for two cases?

Ans.From Perfect gas equation; 

For a given temperature, therefore when the gas is heated in a small vessel (Volume V₁) , the pressure will increases more rapidly than when heated in a large vessel (Volume V₂). As a result, the slope of P – T graph will be more in case of small vessel than that of large vessel.

2.Derive the Boyle’s law using kinetic theory of gases?

Ans.According to Boyle’s law, temperature remaining constant, the volume v of a given mass of a gas is inversely proportional to the pressure P i.e. PV = constant.

Now, according to kinetic theory of gases, the pressure exerted by a gas is given by:-

P = Pressure

V = Volume

= Average Velocity

m = Mass of 1 molecule

N = No. of molecules

M = mN (Mass of gas)

3.At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the r.m.s speed of a helium gas atom at- 20⁰C? Given Atomic Mass of Ar = 39.9 and

of He = 4.0?

Ans.Suppose, Vr.m.s. and V¹r.m.s. are the root mean square speeds of Argon and helium atoms at temperature T and T¹ respectively.

R = Universal Gas constant

T = Temperature

M = Atomic Mass of Gas

Now, Vr.m.s. = 

Now, M = Mass of Argon = 39.9

M¹ = Mass of Helium = 4.0

T¹ = Temperature of helium = -20⁰C

T¹ = 273 + (-20) = 253 K.

T = Temperature of Argon = ?

Since Vr.m.s. =  

Squaring both side,

Putting the values of 

4.Show that constant – temperature bulk modulus K of an ideal gas is the pressure P of the gas?

Ans.When a substance is subjected to a Pressure increase ∆P will undergo a small fractional volume decrease That is related to bulk modulus K by :-

Negative sign indicates decrease in volume. In case of an ideal gas at constant temperature before compression,

M = Molecular Mass of gas

After compression at constant temperature,

From equation 2)

or 

We are concerned with only a small fractional changes. Therefore, is much smaller than 1, As a result, it can be neglected as compared to 1.

Substituting this value of in equation 1) we get

Hence, bulk modulus of an ideal gas is equal to the pressure of the gas in compression carried out at constant temperature.

5.The earth with out its atmosphere would be inhospitably cold. Explain Why?

Ans.The lower layers of earth’s atmosphere reflect infrared radiations from earth back to the surface of earth. Thus the heat radiations received by the earth from the sun during the day are kept trapped by the atmosphere. If atmosphere of earth were not there, its surface would become too cold to live.

6.If a vessel contains 1 mole of O₂ gas (molar mass 32) at temperature T. The pressure of the gas is P. What is the pressure if an identical vessel contains 1 mole of He at a temperature 2 T?

Ans.By ideal gas equation :→

Now, 

Hence 

Now, according to question:→

Using above equations in equation 1)

P₂ = 2P

Hence pressure gets doubled.

7.At very low pressure and high temperature, the real gas behaves like ideal gas. Why?

Ans.An ideal gas is one which has Zero volume of molecule and no intermolecular forces. Now:

1) At very low pressure, the volume of gas is large so that the volume of molecule is negligible compared to volume of gas.

2) At very high temperature, the kinetic energy of molecules is very large and effect of intermolecular forces can be neglected.

Hence real gases behave as an ideal gas at low pressure and high temperature.

8.Calculate the degree of freedom for monatomic, diatomic and triatomic gas?

Ans .The degrees of freedom of the system is given by:-   f = 3 N – K

Where, f = degrees of freedom

N = Number of Particles in the system.

K = Independent relation among the particles.

1) For a monatomic gas; N = 1 and K = 0

f = 3 X 1 – 0 = 3

2) For a diatomic gas ; N = 2 and K = m1

f = 3 X 2 – 1 = 5

3) For a triatomic gas; N = 3 and K = 3

f = 3 X 3 – 3

f = 6

9.Determine the volume of 1 mole of any gas at s. T. P., assuming it behaves like an ideal gas?

Ans.From ideal gas equation:

P = Pressure

V = Volume

n = No. of moles of gas

R = Universal Gas Constant

T = Temperature

PV = nRT

V = 

Here n = 1 mole; R = 8:31 J/mol/K ; T = 273K

P = 1.01 × 10⁵ N|m²

Since 1 litre

Hence  V = 22.4 l

i.e. 1 mol of any gas has a volume of 22.4l at S. T. P. (Standard Temperature & Pressure).

10. A tank of volume 0.3m³ contains 2 moles of Helium gas at 20⁰C. Assuming the helium behave as an ideal gas;

1) Find the total internal energy of the system.

2) Determine the r. m. s. Speed of the atoms.

Ans .1) n = No. of moles = 2

T = Temperature = 273+20 = 293K

R = Universal Gas constant = 8.31 J/mole.

Total energy of the system = E = 

2) Molecular Mass of helium = 4 g | mol

Root Mean speed = Vr.m.s  

Vr.m.s. = 1.35X10³ m|s