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#Charles's law

8 public questions tagged with this topic.

Partial Pressures and Gas Mixtures

A gas at 2 atm and 300 K has a volume of 5 litres. If the temperature rises to 600 K at constant pressure, what is the n

**Gas mixtures** ideal gas law applies to each component, P_total = Σ n_i R T/V, partial pressure P_i = n_i R T/V, mole tion X_i = n_i/n_total, P_i = X_i P_total, enabling calculation of individual pressures from composition, important for kinetic theory and chemistry. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 5 litres, T₁ = 300 K, T₂ = 600 K.V₂ = V₁ × (T₂)/(T₁) = 5 × (600)/(300) = 10 litres. Substituting values gives 10.0 litres, 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 > Partial Pressures and Gas Mixtures

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Collision Frequency and Mean Free Path Variation

A gas at 3 atm and 300 K has a volume of 10 litres. If the temperature rises to 900 K at constant pressure, what is the

**Collision frequency** Z = n σ v_rel, σ = π d² cross-section, v_rel = √2 v_avg, so Z ∝ n, for air at STP n≈2.5×10²⁵ m⁻³ d≈3×10⁻¹⁰ m λ≈68 nm, collision frequency ~10⁹ s⁻¹, illustrating frequent collisions at atmospheric pressure. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 10 litres, T₁ = 300 K, T₂ = 900 K.V₂ = V₁ × (T₂)/(T₁) = 10 × (900)/(300) = 30 litres. Substituting values gives 30 litres, 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 > Collision Frequency and Mean Free Path Variation

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Molecular Mass Density and Ideal Gas Equation

A gas at 1 atm and 273 K has a volume of 15 litres. If the temperature increases to 819 K at constant pressure, what is

**Molecular mass and density** relation ρ = P M/(R T) allows density calculation, ideal gas law also P = n k_B T where n number density, molecular mass determines mass per molecule, density increases with pressure and decreases with temperature, inverse T dependence. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 15 litres, T₁ = 273 K, T₂ = 819 K.V₂ = V₁ × (T₂)/(T₁) = 15 × (819)/(273) = 45 litres. Substituting values gives 45 litres, 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 > Molecular Mass Density and Ideal Gas Equation

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Degrees of Freedom and Molar Specific Heat

A gas at 2 atm and 400 K has a volume of 8 litres. If the temperature decreases to 200 K at constant pressure, what is t

**Specific heat relation** C_p - C_v = R for ideal gas per mole, Mayer's relation, due to work done at constant pressure, degrees of freedom include translational, rotational, vibrational, each quadratic term contributes ½ R to C_v. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 8 litres, T₁ = 400 K, T₂ = 200 K.V₂ = V₁ × (T₂)/(T₁) = 8 × (200)/(400) = 4 litres. Substituting values gives 4 litres, 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 > Degrees of Freedom and Molar Specific Heat

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Gas Laws and Volume-Temperature Relations

A gas at 2 atm and 400 K has a volume of 10 litres. If the temperature decreases to 100 K at constant pressure, what is

**Charles' law** V₁/T₁ = V₂/T₂ at constant pressure, volume proportional to absolute temperature (K), Gay-Lussac P₁/T₁ = P₂/T₂ at constant volume, Boyle's law P₁V₁ = P₂V₂ at constant temperature, combined ideal gas law P V = n R T, R=8.314 J/mol·K. For V₁=24 L T₁=300 K T₂=600 K, V₂= V₁ T₂/T₁=48 L, volume doubles when T doubles at constant P. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 10 litres, T₁ = 400 K, T₂ = 100 K.V₂ = V₁ × (T₂)/(T₁) = 10 × (100)/(400) = 2.5 litres. Substituting values gives 2.5 litres, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Gas Laws and Volume-Temperature Relations

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Specific Heat and Calorimetry

Which law explains why the volume of a gas increases when its temperature rises at constant pressure?

Charles’ Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (V/T = constant, Section 10.4). As per NCERT, applying relevant law/formula with correct units and sign convention leads to Charles’ Law. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Thermal Expansion of Solids and Liquids

What happens to the temperature of an ideal gas if its volume doubles at constant pressure?

Charles’ Law states that at constant pressure, V/T = constant. If volume doubles (V2 = 2V1), the absolute temperature doubles (T2 = 2T1). As per NCERT, applying relevant law/formula with correct units and sign convention leads to It doubles. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Temperature Scales and Triple Point

What happens to the volume of an ideal gas if its temperature is doubled at constant pressure?

For an ideal gas at constant pressure, Charles’ Law states that volume is directly proportional to absolute temperature. If temperature doubles, volume doubles. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It halves. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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