Chapter 11Heat & Thermodynamics

Effective Study Strategies

• Master temperature scale conversions: °C to K: T(K) = T(°C) + 273.15. °C to °F: F = (9/5)C + 32. Know absolute zero = 0K = -273.15°C.
• Understand kinetic theory postulates: Gas molecules move randomly, collisions are elastic, pressure arises from molecular impacts on walls.
• Memorize key gas law formulas: Boyle’s: P₁V₁ = P₂V₂ (T constant). Charles: V₁/T₁ = V₂/T₂ (P constant). Gay-Lussac: P₁/T₁ = P₂/T₂ (V constant).
• Differentiate thermodynamic processes: Isothermal (T constant), Adiabatic (Q=0), Isochoric (V constant), Isobaric (P constant). Know PV diagrams for each.
• Apply first law of thermodynamics: ΔU = Q – W. Sign conventions: +Q = heat added to system, +W = work done by system, +ΔU = internal energy increases.
• Calculate RMS velocity: v_rms = √(3RT/M) = √(3P/ρ). For same T, lighter molecules move faster: v ∝ 1/√M.
• Understand specific heats: C_v for constant volume, C_p for constant pressure. For monoatomic: C_v = (3/2)R, C_p = (5/2)R, γ = 5/3.
• Master Carnot engine efficiency: η = 1 – T₂/T₁ (T₁ = hot reservoir, T₂ = cold reservoir). Maximum possible efficiency.

Exam Preparation Tips

• Practice PV diagram interpretations: Work done = area under curve. Clockwise cycle = net work done by system, counterclockwise = net work done on system.
• Memorize important constants: R = 8.314 J/mol·K, k = 1.38×10⁻²³ J/K, N_A = 6.022×10²³ mol⁻¹, triple point of water = 273.16K.
• Solve numerical problems systematically: 1) Identify process type, 2) Apply appropriate gas law, 3) Use first law ΔU = Q – W, 4) Calculate work using W = ∫PdV.
• Understand entropy concepts: ΔS = Q_rev/T. Entropy increases in natural processes. Heat death of universe when entropy maximum.
• Compare different gas types: Monoatomic (He, Ne): 3 translational DOF. Diatomic (O₂, N₂): 5 DOF (3 trans + 2 rot). Polyatomic: 6+ DOF.
• Practice efficiency calculations: Real engines: 25-40%, Carnot: theoretical max. η = W/Q_h = (Q_h – Q_c)/Q_h = 1 – Q_c/Q_h.
• Draw process cycles: Carnot cycle: two isotherms + two adiabatics. Otto cycle (petrol): adiabatic compression, constant volume heating, adiabatic expansion, constant volume cooling.

Common Pitfalls to Avoid

• Confusing heat (energy transfer) with temperature (measure of hotness)
• Using wrong sign conventions in first law: ΔU = Q – W (W = work done BY system)
• Mixing up C_v and C_p values for different gas types
• Forgetting that adiabatic process means Q=0, not ΔT=0
• Using Celsius instead of Kelvin in gas law calculations (T must be in K)
• Confusing RMS velocity with average or most probable velocity
• Thinking Carnot efficiency can be 100% (requires T_c = 0K, impossible)
• Miscalculating work from PV diagrams (area under curve, with correct sign)