Kinetic Theory of Gases — DPP 3

20 NEET questions from Kinetic Theory of Gases, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

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1
A vessel of volume 8 litre contains an ideal gas at 300 K and 2 atm pressure. The gas is allowed to leak till pressure becomes 125 kpa. Calculate amount of moles which leak out, if temperature remains constant-
  1. A 0.4 moles
  2. B 0.24 moles
  3. C 0.34 moles
  4. D 0.14 moles
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Correct answer: B

2
Air is filled at $60 ^ { \circ } \mathrm { C }$ in a vessel of open mouth. The vessel is heated to a temperature T so that 1/4 th of air escapes. Assuming the volume of the vessel remaining constant the value of T is
  1. A $80 ^ { \circ } \mathrm { C }$
  2. B $444 ^ { \circ } \mathrm { C }$
  3. C $333 ^ { \circ } \mathrm { C }$
  4. D $171 ^ { \circ } \mathrm { C }$
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Correct answer: D

3
On increasing the temperature of a gas filled in a closed container by $2 ^ { \circ } \mathrm { C }$, its pressure increase by 0.4%, then initial temperature of the gas is-
  1. A $50 ^ { \circ } \mathrm { C }$
  2. B $500 ^ { \circ } \mathrm { C }$
  3. C 500 K
  4. D $5000 ^ { \circ } \mathrm { C }$
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Correct answer: C

4
Average momentum of an ideal gas depends upon
  1. A Temperature
  2. B Mass
  3. C Volume
  4. D It is Zero
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Correct answer: D

5
For an ideal gas
  1. A $\mathrm { C } _ { \mathrm { P } } < \mathrm { C } _ { \mathrm { V } }$
  2. B $\mathrm { C } _ { \mathrm { p } } = \mathrm { C } _ { \mathrm { V } }$
  3. C $\mathrm { C } _ { \mathrm { P } } > \mathrm { C } _ { \mathrm { V } }$
  4. D $\mathrm { C } _ { \mathrm { P } } = \mathrm { C } _ { \mathrm { V } } = 0$
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Correct answer: C

6
A balloon is filled at $27 ^ { \circ } \mathrm { C }$ and 1 atm pressure by 500 m$^{3}$ of He. At $- 3 ^ { \circ } \mathrm { C }$ and 0.5 atm pressure, the volume (in m$^{3}$) of He gas contained in balloon will be
  1. A 500
  2. B 850
  3. C 900
  4. D 895
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Correct answer: C

7
Which of the following statement given below are correct for monoatomic gas?
I. $\mathrm { C } _ { \mathrm { v } } = \frac { 3 } { 2 } \mathrm { R }$
II. $\mathrm { C } _ { \mathrm { P } } = \frac { 5 } { 2 } \mathrm { R }$
III. $\mathrm { C } _ { \mathrm { p } } - \mathrm { C } _ { \mathrm { V } } = 2 \mathrm { R }$
IV. $\frac { \mathrm { C } _ { \mathrm { P } } } { \mathrm { C } _ { \mathrm { V } } } = \frac { 5 } { 3 }$
  1. A I only
  2. B I, II and IV
  3. C III only
  4. D I, II, III and IV
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Correct answer: B

8
1 L of an ideal gas at $27 ^ { \circ } \mathrm { C }$ is heated at a constant pressure to the $297 ^ { \circ } \mathrm { C }$. Then, the final volume is approximately:
  1. A 1.2 L
  2. B 1.9 L
  3. C 19 L
  4. D 2.4 L
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Correct answer: B

9
What is the mass of 2 L of N₂ at 22.4 atm pressure and 273 K?
  1. A 28 g
  2. B 14 × 22.4 g
  3. C 56 g
  4. D 15 g
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Correct answer: C

10
If γ is the ratio of specific heats and R is the universal gas constant, then the molar specific heat at constant volume C$_{V}$ is given by
  1. A γR
  2. B $\frac { ( \gamma - 1 ) R } { \gamma }$
  3. C $\frac { \mathrm { R } } { \gamma - 1 }$
  4. D $\frac { \gamma \mathrm { R } } { \gamma - 1 }$
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Correct answer: C

11
Volume of gas becomes four times if
  1. A Temperature become four times at constant pressure
  2. B Temperature become one fourth at constant pressure
  3. C Temperature becomes two times at constant pressure
  4. D Temperature becomes half at constant pressure
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Correct answer: A

12
Air inside a closed container is saturated with vapour pressure of water is P. If the mixture is compressed to one-half of its volume by maintaining constant temperature the pressure becomes
  1. A Twice
  2. B Thrice
  3. C No effect
  4. D Quadrupled
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Correct answer: A

13
At a pressure of $24 \times 10 ^ { 5 }$ dyne $/ \mathrm { cm } ^ { 2 }$, the volume of O₂ is 10 litre and mass is 20 gm. The r.m.s velocity will be
  1. A 800 m/sec
  2. B 400 m/sec
  3. C 600 m/sec
  4. D 200 m/sec
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Correct answer: C

14
At a certain temperature, the r.m.s. velocity for O₂ is 400 m/sec. At the same temperature, the r.m.s veloctiy for H₂ molecules will be
  1. A 100 m/s
  2. B 25 m/s
  3. C 1600 m/s
  4. D 6400 m/s
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Correct answer: C

15
In the given V–T diagram, what is the relation between pressure P$_{1}$ and P$_{2}$?
Kinetic Theory of Gases – NEET-11282
  1. A P$_{1}$ = P$_{2}$
  2. B P$_{2}$ > P$_{1}$
  3. C P$_{1}$ > P$_{2}$
  4. D Data insufficient
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Correct answer: C

16
Mean free path of molecules of a gas is inversely proportional to (r is the radius of the molecule)
  1. A r
  2. B r$^{3}$
  3. C r$^{2}$
  4. D $\mathrm { r } ^ { 1 / 2 }$
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Correct answer: C

17
The molecules of a given mass of a gas have r.m.s. velocity of 200 m/sec at $27 ^ { \circ } \mathrm { C }$ and $1.0 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ pressure. When the temperature is $127 ^ { \circ } \mathrm { C }$ and pressure is $0.5 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$, the r.m.s velocity in m/sec will be
  1. A $\frac { 100 \sqrt { 2 } } { 3 }$
  2. B $100 \sqrt { 2 }$
  3. C $\frac { 400 } { \sqrt { 3 } }$
  4. D 400
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Correct answer: C

18
A gas at the temperature 250 K is contained in a closed vessel. If the gas is heated through 1 K, then the percentage increase in its pressure will be
  1. A 0.4%
  2. B 0.2%
  3. C 0.1%
  4. D 0.8%
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Correct answer: A

19
For a gas molecule with 6 degrees of freedom, the law of equipartition of energy gives the following relation between the molecular specific heat (C$_{V}$) and gas constant (R)
  1. A $\mathrm { C } _ { \mathrm { v } } = \frac { \mathrm { R } } { 2 }$
  2. B $\mathrm { C } _ { \mathrm { V } } = \mathrm { R }$
  3. C $\mathrm { C } _ { \mathrm { V } } = 2 \mathrm { R }$
  4. D $\mathrm { C } _ { \mathrm { V } } = 3 \mathrm { R }$
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Correct answer: D

20
A closed vessel contains 8 gm of oxygen and 7 gm of nitrogen. The total pressure is 10 atm at the given temperature. If all the oxygen is removed from the system without permitting any change in temperature, then the pressure will become (in atmospheres):
  1. A 70/15
  2. B 80/15
  3. C 5
  4. D 70/8
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Correct answer: C

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