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NCERT Solutions › Physics › Chapter 13

Chapter 13: Kinetic Theory

NCERT Solutions for CBSE Class 10 Physics — 97 solved questions with detailed explanations.

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Solved Questions

Q1. The average kinetic energy of a gas molecule at temperature T is:

Difficulty: Easy · Topic: Kinetic Energy

Solution

Average KE per molecule = (3/2)kT, where k is Boltzmann constant.

Q2. The mean free path of a gas molecule depends on:

Difficulty: Easy-Medium · Topic: Mean Free Path

Solution

Mean free path λ = 1/(√2 π d² n), where d is molecular diameter and n is number density.

Q3. For a diatomic gas at room temperature, the ratio of specific heats γ = C_p/C_v is:

Difficulty: Easy-Medium · Topic: Specific Heats

Solution

Diatomic gas has 5 degrees of freedom (3 translational + 2 rotational). C_v = 5R/2, C_p = 7R/2. γ = 7/5.

Q4. The degrees of freedom of a monatomic gas (e.g., He, Ar) are:

Difficulty: Easy-Medium · Topic: Degrees of Freedom

Solution

A monatomic gas (e.g., He, Ar) has 3 degrees of freedom at room temperature.

Q5. The degrees of freedom of a diatomic gas at room T (e.g., N₂, O₂) are:

Difficulty: Easy-Medium · Topic: Degrees of Freedom

Solution

A diatomic gas at room T (e.g., N₂, O₂) has 5 degrees of freedom at room temperature.

Q6. The degrees of freedom of a linear triatomic gas at room T are:

Difficulty: Easy-Medium · Topic: Degrees of Freedom

Solution

A linear triatomic gas at room T has 7 degrees of freedom at room temperature.

Q7. The rms speed of hydrogen molecules at 300 K is approximately (M_H2 = 2 g/mol, R = 8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3 × 8.314 × 300/0.002) = √(3741300) ≈ 1934 m/s ≈ 1920 m/s.

Q8. The rms speed of O₂ molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/32×10⁻³) ≈ 483.6 m/s.

Q9. The rms speed of N₂ molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/28×10⁻³) ≈ 516.9 m/s.

Q10. The rms speed of He molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/4×10⁻³) ≈ 1367.7 m/s.

Q11. The rms speed of H₂ molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/2×10⁻³) ≈ 1934.2 m/s.

Q12. The rms speed of CO₂ molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/44×10⁻³) ≈ 412.4 m/s.

Q13. The rms speed of Ar molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/40×10⁻³) ≈ 432.5 m/s.

Q14. The rms speed of Ne molecules at 300 K is approximately (R=8.314 J/mol·K):

Difficulty: Medium · Topic: RMS Speed

Solution

v_rms = √(3RT/M) = √(3×8.314×300/20×10⁻³) ≈ 611.7 m/s.

Q15. RMS speed of gas (M=2 g/mol) at 300 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q16. RMS speed of gas (M=4 g/mol) at 350 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q17. RMS speed of gas (M=6 g/mol) at 400 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q18. RMS speed of gas (M=8 g/mol) at 450 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q19. RMS speed of gas (M=10 g/mol) at 500 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q20. RMS speed of gas (M=12 g/mol) at 550 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q21. RMS speed of gas (M=14 g/mol) at 600 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q22. RMS speed of gas (M=16 g/mol) at 650 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q23. RMS speed of gas (M=18 g/mol) at 700 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q24. RMS speed of gas (M=20 g/mol) at 750 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q25. RMS speed of gas (M=22 g/mol) at 800 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q26. RMS speed of gas (M=24 g/mol) at 850 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q27. RMS speed of gas (M=26 g/mol) at 900 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q28. RMS speed of gas (M=28 g/mol) at 950 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q29. RMS speed of gas (M=30 g/mol) at 1000 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q30. RMS speed of gas (M=32 g/mol) at 1050 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q31. RMS speed of gas (M=34 g/mol) at 1100 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q32. RMS speed of gas (M=36 g/mol) at 1150 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q33. RMS speed of gas (M=38 g/mol) at 1200 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q34. RMS speed of gas (M=40 g/mol) at 1250 K is (R=8.314):

Difficulty: Medium · Topic: RMS Speed

Solution

v = √(3RT/M).

Q35. RMS speed: M=2g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1579.3 m/s.

Q36. RMS speed: M=2g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1765.7 m/s.

Q37. RMS speed: M=2g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1934.2 m/s.

Q38. RMS speed: M=2g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=2089.2 m/s.

Q39. RMS speed: M=2g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=2233.5 m/s.

Q40. RMS speed: M=2g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=2497.1 m/s.

Q41. RMS speed: M=2g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=2735.4 m/s.

Q42. RMS speed: M=4g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1116.7 m/s.

Q43. RMS speed: M=4g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1248.5 m/s.

Q44. RMS speed: M=4g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1367.7 m/s.

Q45. RMS speed: M=4g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1477.3 m/s.

Q46. RMS speed: M=4g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1579.3 m/s.

Q47. RMS speed: M=4g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1765.7 m/s.

Q48. RMS speed: M=4g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=1934.2 m/s.

Q49. RMS speed: M=16g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=558.4 m/s.

Q50. RMS speed: M=16g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=624.3 m/s.

Q51. RMS speed: M=16g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=683.9 m/s.

Q52. RMS speed: M=16g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=738.7 m/s.

Q53. RMS speed: M=16g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=789.7 m/s.

Q54. RMS speed: M=16g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=882.9 m/s.

Q55. RMS speed: M=16g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=967.1 m/s.

Q56. RMS speed: M=17g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=541.7 m/s.

Q57. RMS speed: M=17g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=605.6 m/s.

Q58. RMS speed: M=17g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=663.4 m/s.

Q59. RMS speed: M=17g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=716.6 m/s.

Q60. RMS speed: M=17g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=766.1 m/s.

Q61. RMS speed: M=17g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=856.5 m/s.

Q62. RMS speed: M=17g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=938.2 m/s.

Q63. RMS speed: M=20g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=499.4 m/s.

Q64. RMS speed: M=20g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=558.4 m/s.

Q65. RMS speed: M=20g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=611.7 m/s.

Q66. RMS speed: M=20g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=660.7 m/s.

Q67. RMS speed: M=20g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=706.3 m/s.

Q68. RMS speed: M=20g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=789.7 m/s.

Q69. RMS speed: M=20g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=865.0 m/s.

Q70. RMS speed: M=28g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=422.1 m/s.

Q71. RMS speed: M=28g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=471.9 m/s.

Q72. RMS speed: M=28g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=516.9 m/s.

Q73. RMS speed: M=28g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=558.4 m/s.

Q74. RMS speed: M=28g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=596.9 m/s.

Q75. RMS speed: M=28g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=667.4 m/s.

Q76. RMS speed: M=28g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=731.1 m/s.

Q77. RMS speed: M=32g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=394.8 m/s.

Q78. RMS speed: M=32g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=441.4 m/s.

Q79. RMS speed: M=32g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=483.6 m/s.

Q80. RMS speed: M=32g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=522.3 m/s.

Q81. RMS speed: M=32g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=558.4 m/s.

Q82. RMS speed: M=32g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=624.3 m/s.

Q83. RMS speed: M=32g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=683.9 m/s.

Q84. RMS speed: M=40g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=353.1 m/s.

Q85. RMS speed: M=40g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=394.8 m/s.

Q86. RMS speed: M=40g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=432.5 m/s.

Q87. RMS speed: M=40g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=467.2 m/s.

Q88. RMS speed: M=40g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=499.4 m/s.

Q89. RMS speed: M=40g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=558.4 m/s.

Q90. RMS speed: M=40g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=611.7 m/s.

Q91. RMS speed: M=44g/mol, T=200K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=336.7 m/s.

Q92. RMS speed: M=44g/mol, T=250K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=376.5 m/s.

Q93. RMS speed: M=44g/mol, T=300K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=412.4 m/s.

Q94. RMS speed: M=44g/mol, T=350K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=445.4 m/s.

Q95. RMS speed: M=44g/mol, T=400K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=476.2 m/s.

Q96. RMS speed: M=44g/mol, T=500K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=532.4 m/s.

Q97. RMS speed: M=44g/mol, T=600K:

Difficulty: Medium · Topic: RMS

Solution

v=√(3RT/M)=583.2 m/s.

Other Chapters in Physics

Ch 1: Physical WorldCh 2: Units & MeasurementsCh 3: Motion in a Straight LineCh 4: Motion in a PlaneCh 5: Laws of MotionCh 6: Work Energy & PowerCh 7: System of ParticlesCh 8: GravitationCh 9: Mechanical Properties of SolidsCh 10: Mechanical Properties of FluidsCh 11: Thermal Properties of MatterCh 12: ThermodynamicsCh 14: OscillationsCh 15: Waves

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