Kinetic Theory of Gases

Answer

Formula: P = (1/3) × ρ × c̄² Where: • P = Pressure exerted by the gas (Pa) • ρ = Density of the gas (kg/m³) • c̄² = Mean square speed of molecules (m²/s²) Alternate form: PV = (1/3) × M × c̄² Where …

Answer

Given: • N = 10²², m = 5 × 10⁻²⁶ kg, l = 10 cm = 0.10 m, u = 500 m/s Step 1 – Change in momentum per collision: 2mu = 2 × 5×10⁻²⁶ × 500 = 5×10⁻²³ kg·m/s Step 2 – Time between successive impacts: t =…

Answer

1. A gas has a very large number of identical rigid molecules moving randomly with all possible velocities. Intermolecular forces are negligible. 2. Collisions between molecules and with walls are pe…

Answer

These are two different mathematical quantities and are NOT equal in general. Example: Five molecules with speeds 1, 2, 3, 4, 5 units. Mean speed: c̄ = (1+2+3+4+5)/5 = 15/5 = 3 units (c̄)² = 9 Mean…

Answer

Given: • T = 300 K • m = 3.347 × 10⁻²⁷ kg • k = 1.38 × 10⁻²³ J/K Formula: c_rms = √(3kT/m) Step 1 – Numerator: 3kT = 3 × 1.38×10⁻²³ × 300 = 3 × 4.14×10⁻²¹ = 1.242×10⁻²⁰ J Step 2 – Divide by mass: 1…

Answer

Given: • Initial temperature T₀ = 273 K • Required: c_rms = 2 × c₀ (double the initial RMS speed) Key relation: c_rms ∝ √T Step 1 – Set up ratio: c/c₀ = √(T/T₀) 2c₀/c₀ = √(T/273) 2 = √(T/273) Step …

Answer

Kinetic Interpretation of Temperature: The mean kinetic energy of a gas molecule depends ONLY on the absolute temperature T and is independent of its mass. Formula: (1/2)mc̄² = (3/2)kT Where k = Bol…

Answer

Given: • T = 300 K • k = 1.38 × 10⁻²³ J/K Formula: Ē = (3/2)kT Step 1 – Substitute values: Ē = (3/2) × 1.38×10⁻²³ × 300 Step 2 – Calculate: Ē = 1.5 × 4.14×10⁻²¹ Ē = 6.21×10⁻²¹ J Answer: Ē = 6.21 ×…