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#gas physics

3 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

Why does the speed of sound increase with temperature in a gas?

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. Speed of sound in a gas is v = √((gamma P/rho)) , and since P/rho ∝ T (ideal gas law), higher temperature increases molecular velocity, thus increasing v . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Molecular velocity increases, illustrating frequency-length-speed interdependence and quantization by

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

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Degrees of Freedom and Molar Specific Heat

The number density of a gas is 2.5 × 10²⁵ m⁻³. If the molecular diameter is 2 × 10⁻¹⁰ m, what is the mean free path?

**Degrees of freedom** f counts independent motions, monatomic 3 translational, diatomic 3 translational +2 rotational =5 at room T, vibrational adds at high T, molar specific heat at constant volume C_v = f/2 R, at constant pressure C_p = C_v + R, ratio γ = C_p/C_v = (f+2)/f, monatomic γ=5/3≈1.67, diatomic γ=7/5=1.4. l = (1)/(√(2) n π d²).n = 2.5 × 10²⁵, d = 2 × 10⁻¹⁰, π ≈ 3.14.l = (1)/(1.414 × 2.5 × 10²⁵) × 3.14 × (2 × 10⁻¹⁰)² = (1)/(4.44 × 10¹⁷) ≈ 2.25 × 10⁻⁷ m . Substituting values gives 2.25 × 10⁻⁷ m, which matches expected kinetic theory result,

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Degrees of Freedom and Molar Specific Heat

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Mean Free Path and Molecular Diameter

The mean free path of a gas molecule is 4 × 10⁻⁷ m at 2 atm. What will it be at 4 atm if temperature remains constant?

**Kinetic theory mean free path** λ = 1/(√2 π d² n) quantifies collision frequency. With n =1.0×10²⁵ m⁻³, λ=9×10⁻⁷ m, d² =1/(1.414×10²⁵×3.14×9×10⁻⁷)=2.5×10⁻²⁰ m², d≈1.58×10⁻¹⁰ m, typical molecular size ~10⁻¹⁰ m, consistent with gas kinetic theory. l ∝ (1)/(n), n ∝ P. If P doubles, n doubles, l halves.New l = 4 × 10⁻⁷/2 = 2 × 10⁻⁷ m. Substituting values gives 2 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Mean Free Path and Molecular Diameter

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