CBSE Class 11 Kinetic Theory of Gases Worksheet A

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Question. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0JK^–1. If the speed of sound in this gas at NTP is 952 ms^–1, then the heat capacity at constant pressure is (Take gas constant R = 8.3 JK^–1 mol^–1) 
(a) 7.5 JK^–1 mol^–1
(b) 7.0 JK^–1 mol^–1
(c) 8.5 JK^–1 mol^–1
(d) 8.0 JK^–1 mol^–1

Answer: D

Question. Gases exert pressure on the walls of the container because the gas molecules
(a) possess momentum
(b) collide with each other
(c) have finite volume
(d) obey gas laws.

Answer: A

Question. In the kinetic theory of gases, which of these statements is/are true ?
(i) The pressure of a gas is proportional to the mean speed of the molecules.
(ii) The root mean square speed of the molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the mean speed of the molecules.
(iv) The mean translational kinetic energy of a gas is proportional to its kelvin temperature.
(a) (ii) and (iii) only
(b) (i),(ii)and (iv) only
(c) (i) and (iii) only
(d) (iii) and (iv) only 

Answer: D

Question. In the given (V – T) diagram, what is the relation between pressure P₁ and P₂ ? 

(a) P₂ > P₁
(b) P₂ < P₁
(c) Cannot be predicte
(d) P₂ = P₁

Answer: B

Question. The molar heat capacities of a mixture of two gases at constant volume is 13R/6. The ratio of number of moles of the first gas to the second is 1 : 2. The respective gases may be
(a) O₂ and N₂
(b) He and Ne
(c) He and N₂
(d) N₂ and He

Answer: C

Question. Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient) when it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be
(a) √2 times
(b) 2 times
(c) unchanged
(d) half

Answer: B

Question. One mole of a gas occupies 22.4 lit at N.T.P. Calculate the difference between two molar specific heats of the gas. J = 4200 J/kcal.
(a) 1.979 k cal/kmol K
(b) 2.378 k cal/kmol K
(c) 4.569 kcal/kmol K
(d) 3.028 k cal/ kmol K

Answer: A

Question. Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec. The root mean square speed of these molecules (in km/sec) is
(a) √54 / 4
(b) √54 / 2
(c) 3.5
(d) 3 √3

Answer: A

Question. The density of air at pressure of 10⁵ Nm^–2 is 1.2 kg m^–3. Under these conditions, the root mean square velocity of the air molecules in ms^–1 is
(a) 500
(b) 1000
(c) 1500
(d) 3000

Answer: A

Question. At what temperature, pressure remaining constant, will the r.m.s. velocity of a gas be half of its value at 0ºC?
(a) 0ºC
(b) –273ºC
(c) 32ºC
(d) –204ºC

Answer: D

Question. How many degrees of freedom are associated with 2 grams of He at NTP ?
(a) 3
(b) 3.01 × 10²³
(c) 9.03 × 10²³
(d) 6

Answer: C

Question. The r.m.s. velocity of oxygen molecule at 16ºC is 474 m/sec. The r.m.s. velocity in m/s of hydrogen molecule at 127ºC is
(a) 1603
(b) 1896
(c) 2230.59
(d) 2730

Answer: C

Question. A sample of an ideal gas occupies a volume of V at a pressure P and absolute temperature. T. The mass of each molecule is m. The equation for density is
(a) m k T
(b) P/k T
(c) P/(k T V)
(d) P m/k T

Answer: D

Question. At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is (T = absolute temperature of the gas) is
(a) T²
(b) T
(c) 1/T
(d) 1/T2

Answer: C

Question. The K.E. of one mole of an ideal gas is E = (3/2) RT. Then Cp will be
(a) 0.5 R
(b) 0.1 R
(c) 1.5 R
(d) 2.5 R

Answer: D

Question. If 2 mole of an ideal monatomic gas at temperature T₀ is mixed with 4 moles of another ideal monatomic gas at temperature 2T₀, then the temperature of the mixture is
(a) 5/3 T₀
(b) 3/2 T₀
(c) 4/3 T₀
(d) 5/4 T0

Answer: A

Question. The temperature at which the root mean square velocity of the gas molecules would become twice of its value at 0°C is
(a) 819°C
(b) 1092°C
(c) 1100°C
(d) 1400°C

Answer: A

Question. The gases are at absolute temperature 300ºK and 350ºK respectively. The ratio of average kinetic energy of their molecules is
(a) 7 : 6
(b) 6 : 7
(c) 36 : 49
(d) 49 : 36

Answer: B

Question. At what temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47ºC
(a) 80 K
(b) –73 K
(c) 3 K
(d) 20 K

Answer: D

Question. If masses of all molecule of a gas are halved and their speed doubled then the ratio of initial and final pressure will be
(a) 2 : 1
(b) 1 : 2
(c) 4 : 1
(d) 1 : 4

Answer: B

Question. On a particular day, the relative humidity is 100% and the room temperature is 30ºC, then the dew point is
(a) 70ºC
(b) 30ºC
(d) 100ºC
(d) 0ºC

Answer: B

Question. N molecules, each of mass m, of gas A and 2 N molecules, each of mass 2 m, of gas B are contained in the same vessel which is maintained at a temperature T. The mean square of the velocity of molecules of B type is denoted by v² and the mean square of the X component of the velocity of A type is dentoed by ω², ω²/v² is
(a) 2
(b) 1
(c) 1/3
(d) 2/3

Answer: D

Question. A gas mixture consists of 2 moles of O₂ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is :- 
(a) 15 RT
(b) 9 RT
(c) 11 RT
(d) 4 RT

Answer: C

Question. Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of V_rms of molecules and speed of sound in mixture?
(a) √3/2
(b) √2
(c) √2 /3
(d) √3

Answer: B

Question. The density of a gas is 6 × 10^–2 kg/m³ and the root mean square velocity of the gas molecules is 500 m/s. The pressure exerted by the gas on the walls of the vessel is
(a) 5×10³ N/m²
(b) 1.2×10^–4 N/m²
(c) 0.83×10^–4 N/m²
(d) 30N/m²

Answer: A

1. What is an ideal perfect gas?

2. State Charles’s law? If air is filled in a vessel at 60°c. To what temperature should it be heated in order that

1/3 rd of air may escape out of vessel?

3. Show that average kinetic energy of translation per molecule of gas is directly proportional to the absolute temperature of gas?

4. Air pressure in a car tyre increases during driving? Why?

5. Four molecules of gas have speeds 2, 4, 6, 8, km/s. respectively.

Calculate 1) Average speed

2) Root Mean square speed?

6. Derive Avogadro’s law?

7. What are the assumptions of kinetic theory of gas? 

8. Derive an expression for the pressure due to an ideal gas?

Click on link below to download CBSE Class 11 Kinetic Theory of Gases Worksheet A.