Thermodynamic Processes Overview

Overview

This lecture covers the major thermodynamic processes (isobaric, isochoric, isothermal, adiabatic), their associated equations for work, heat, and internal energy, and techniques for solving related problems, including PV diagrams and efficiency.

Thermodynamic Processes & Equations

Isochoric (Constant Volume)

• ΔV = 0; thus, W = 0 for the process.
• ΔU = Q (since W = 0).
• Q = nCVΔT, where n = moles, CV = molar heat capacity at constant volume, ΔT = change in temperature.

Isobaric (Constant Pressure)

• ΔP = 0; P is constant.
• W = PΔV or W = nRΔT.
• Q = nCPΔT, where CP = molar heat capacity at constant pressure.
• ΔU = Q − W = nCVΔT.

Isothermal (Constant Temperature)

• ΔT = 0; T is constant, so ΔU = 0.
• Q = W.
• W = nRT ln(Vf/Vi) or W = nRT ln(Pi/Pf).

Adiabatic (No Heat Exchange)

• Q = 0 (perfect insulation or very rapid process).
• ΔU = −W = nCVΔT.
• PV^γ = constant; T1V1^(γ−1) = T2V2^(γ−1), where γ = CP/CV.

Thermodynamic Problem-Solving & Concepts

• The first law of thermodynamics: ΔU = Q − W.
• Signs: Q positive if heat enters, negative if it leaves. W positive if work is done by the system, negative if on the system.
• For cyclic processes, the work equals the net heat flow: ΔUcycle = 0, so Q = W.
• Area under or within a PV diagram represents work done; sign indicates direction (clockwise is positive).
• State functions: Pressure, temperature, volume, internal energy depend only on initial/final states, not the path. Work and heat are path-dependent.

Specific Heats & Molar Heat Capacities

• Monoatomic gas: CV ≈ (3/2)R, CP ≈ (5/2)R.
• Diatomic gas: CV ≈ (5/2)R, CP ≈ (7/2)R.
• Polyatomic gas: CV ≈ (7/2)R, CP ≈ (9/2)R.
• Use tables if accurate CV and CP values are needed for non-ideal or complex gases.

Gas Laws & Useful Equations

• Ideal gas law: PV = nRT.
• Charles’s law (isobaric): V1/T1 = V2/T2.
• Gay-Lussac’s law (isochoric): P1/T1 = P2/T2.
• Boyle’s law (isothermal): P1V1 = P2V2.

Efficiency & Energy Flow

• Efficiency = Wout / Qin × 100%
• Qin = total heat absorbed; Qout = heat released.
• In heat engines, net work is positive for clockwise cycles.

Key Terms & Definitions

• Isochoric Process — thermodynamic process at constant volume.
• Isobaric Process — process at constant pressure.
• Isothermal Process — process at constant temperature.
• Adiabatic Process — process with no heat exchange (Q = 0).
• Internal Energy (U) — total energy contained within a system.
• Work (W) — energy transfer via force and displacement.
• Heat (Q) — energy transfer due to temperature difference.
• Molar Heat Capacity (CV, CP) — heat required to raise 1 mole by 1 K at constant volume/pressure.
• Gamma (γ) — ratio CP/CV.
• State Function — property determined by state, not path (e.g., U, P, T, V).
• Path Function — property dependent on the process path (e.g., Q, W).

Action Items / Next Steps

• Review and memorize all key equations for each process.
• Practice solving problems using PV diagrams and the connected equations.
• Look up and note specific heat values for gases if not given.
• Work on additional practice problems for each process type.