Skip to content
Login Register

#gas law

18 public questions tagged with this topic.

Cyclic Processes and Reversibility Concepts

A gas at 6 atm in an 8 L container is cooled from 50°C to 10°C at constant volume. What is the final pressure?

**Reversibility** reversible process can be reversed by infinitesimal change, no entropy production, quasi-static without friction, e.g., Carnot cycle reversible, irreversible processes involve friction, free expansion, heat transfer across finite temperature difference, entropy increases, most real processes irreversible. Isochoric: (P₁)/(T₁) = (P₂)/(T₂) . P₁ = 6 atm , T₁ = 50 + 273 = 323 K , T₂ = 10 + 273 = 283 K . (6)/(323) = (P₂)/(283) ⇒ P₂ = (6 × 283)/(323) ≈ 5.26 atm . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic P

Ref: NCERT > Physics Book > Thermodynamics > Cyclic Processes and Reversibility Concepts

View Details
Isochoric Processes and Pressure-Temperature

0.2 moles of an ideal gas at 360 K are compressed isothermally from 8 L to 2 L. What is the heat released? ( R = 8.3 J m

**Isochoric process** constant volume ΔV=0, work W=0, first law ΔU = Q, all heat goes to internal energy, P/T = constant from ideal gas law P V = n R T at constant V, pressure proportional to temperature, P₁/T₁ = P₂/T₂, e.g., heating gas in rigid container pressure rises proportionally to T. Isothermal: Δ U = 0 , Δ Q = Δ W . W = μ R T ln((V₂)/(V₁)) . μ = 0.2 , T = 360 , V₂ = 2 , V₁ = 8 . W = 0.2 × 8.3 × 360 × ln((2)/(8)) = 597.6 × (-1.386) ≈ -829 J (work by

Ref: NCERT > Physics Book > Thermodynamics > Isochoric Processes and Pressure-Temperature

View Details
Isochoric Processes and Pressure-Temperature

0.15 moles of an ideal gas at 320 K expand isothermally from 3 L to 9 L. What is the work done by the gas? ( R = 8.3 J m

**Pressure-temperature relation** at constant volume Gay-Lussac law P ∝ T, for V constant, P₁/T₁ = P₂/T₂, if T doubles from 300 K to 600 K P doubles, e.g., P₁=1 atm at 300 K P₂=2 atm at 600 K, no work done, ΔU = n C_v ΔT = Q. Isothermal: W = μ R T ln((V₂)/(V₁)) . μ = 0.15 , T = 320 , V₂ = 9 , V₁ = 3 . W = 0.15 × 8.3 × 320 × ln((9)/(3)) = 398.4 × 1.0986 ≈ 438 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W =

Ref: NCERT > Physics Book > Thermodynamics > Isochoric Processes and Pressure-Temperature

View Details
Specific Heat Capacity and Latent Heat

A gas at 3 atm in a 4 L container is heated from 25°C to 75°C at constant volume. What is the final pressure?

**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. Isochoric: (P₁)/(T₁) = (P₂)/(T₂) . P₁ = 3 atm , T₁ = 25 + 273 = 298 K , T₂ = 75 + 273 = 348 K . (3)/(298) = (P₂)/(348) ⇒ P₂ = (3 × 348)/(298) ≈ 3.5 atm . Using first law ΔU = Q - W,

Ref: NCERT > Physics Book > Thermodynamics > Specific Heat Capacity and Latent Heat

View Details
Second Law Heat Engines and Kelvin-Planck

0.4 moles of an ideal gas at 340 K expand adiabatically from 7 atm to 1 atm. If gamma = 1.4 , what is the final temperat

**Carnot engine** reversible engine operating between T_h and T_c has maximum efficiency η =1 - T_c/T_h, T in kelvin, e.g., T_h=400 K T_c=300 K η=0.25, real engines less due to irreversibilities, second law defines direction of spontaneous processes and entropy increase. Adiabatic: T₁ V₁^γ-1 = T₂ V₂^γ-1 , V₁ = (μ R T₁)/(P₁) = (0.4 × 8.3 × 340)/(7) ≈ 161.37 L , V₂ = (0.4 × 8.3 × T₂)/(1) = 3.32 T₂ . 340 × 161.37⁰.4 = T₂ × (3.32 T₂)⁰.4 . Approximate: T₂ ≈ 245 K . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W =

Ref: NCERT > Physics Book > Thermodynamics > Second Law Heat Engines and Kelvin-Planck

View Details
Collision Frequency and Mean Free Path Variation

What is the volume of 0.3 moles of an ideal gas at 2.5 atm and 127°C? (R = 8.31 J mol⁻¹ K⁻¹)

**Mean free path variation** λ ∝1/n ∝1/P at constant T, λ ∝ T/P, temperature increase increases λ because n decreases at constant P, but also v increases, overall λ ∝ T/P, for gas at 2 atm λ=4×10⁻⁷ m, at 4 atm λ=2×10⁻⁷ m halves when pressure doubles, as n doubles. PV = μ R T, V = (μ R T)/(P).T = 127 + 273 = 400 K, P = 2.5 × 1.01 × 10⁵ = 2.525 × 10⁵ Pa.V = (0.3 × 8.31 × 400)/(2.525 × 10⁵) = 3.95 × 10⁻³ m³ ≈ 3.95 litres. Substituting values gives 3.95 litres, which matches expected kinetic theory

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Collision Frequency and Mean Free Path Variation

View Details
RMS Speed and Temperature Dependence

A container holds 0.5 moles of an ideal gas at 2 atm pressure and 27°C. What is the volume of the gas? (R = 8.31 J mol⁻¹

**Temperature dependence of RMS speed** v_rms ∝ √T, doubling T increases v_rms by √2≈1.414, e.g., at 300 K v_rms for O₂ ≈483 m/s, at 600 K ≈683 m/s, illustrating kinetic theory relation between temperature and molecular motion, average kinetic energy ½ m v_rms² =3/2 k_B T. Ideal gas equation: PV = μ R T.T = 27 + 273 = 300 K, P = 2 × 1.01 × 10⁵ Pa = 2.02 × 10⁵ Pa, μ = 0.5 mol.V = (μ R T)/(P) = (0.5 × 8.31 × 300)/(2.02 × 10⁵) = 6.17 × 10⁻³ m³ = 6.17 litres . Substituting values gives 6.2 litres, which

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > RMS Speed and Temperature Dependence

View Details
RMS Speed and Temperature Dependence

A gas occupies 28.0 litres at STP. How many moles are present? (Molar volume at STP = 22.4 litres)

**Maxwell-Boltzmann distribution** gives distribution of speeds, v_rms = √(3kT/m), most probable v_mp = √(2kT/m), average v_avg = √(8kT/πm), all ∝ √T, ratio v_rms:v_avg:v_mp =1.732:1.596:1.414, temperature raises all speeds proportionally. Number of moles (μ) = VolumeMolar volume.μ = (28.0)/(22.4) = 1.25 mol. Substituting values gives 1.25 mol, 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 > RMS Speed and Temperature Dependence

View Details