Introduction
Thermodynamic processes describe transitions in state variables of a system: pressure, volume, temperature, internal energy. They are pathways connecting equilibrium states. Analysis focuses on energy transfers as work and heat under constraints imposed by the first law of thermodynamics.
"Thermodynamics is the only physical theory of universal content which I am convinced will never be overthrown." -- Albert Einstein
Basic Concepts
System and Surroundings
System: defined mass or volume under study. Surroundings: everything external to system boundary. Boundary: interface allowing energy/mass transfer.
State and Path Functions
State functions: properties dependent only on state (e.g., pressure P, volume V, temperature T, internal energy U). Path functions: depend on process path (work W, heat Q).
Equilibrium and Quasi-Static Process
Equilibrium: no net macroscopic changes. Quasi-static: infinitely slow process maintaining near-equilibrium states throughout.
Classification of Processes
Based on Heat Transfer
Adiabatic: no heat exchange (Q=0). Non-adiabatic: heat transfer occurs (Q≠0).
Based on Pressure
Isobaric: constant pressure (ΔP=0). Non-isobaric: pressure varies.
Based on Volume
Isochoric: constant volume (ΔV=0). Non-isochoric: volume varies.
Based on Temperature
Isothermal: constant temperature (ΔT=0). Non-isothermal: temperature varies.
Cyclic
Process returns system to initial state: ΔU=0 over cycle.
Isothermal Process
Definition
Temperature constant (T=const). Internal energy U remains constant for ideal gases.
Energy Transfers
ΔU = 0, thus Q = W (heat absorbed equals work done by system).
Equation for Ideal Gas
PV = constant. Work done:
W = nRT ln(V₂ / V₁)Applications
Slow compression/expansion, thermal reservoirs, phase changes at constant temperature.
Adiabatic Process
Definition
No heat exchange: Q = 0. Energy transfer solely as work.
First Law Formulation
ΔU = W (work done changes internal energy).
Ideal Gas Relations
PV^γ = constantTV^(γ−1) = constantγ = C_p / C_v (heat capacities ratio)Work Done
Calculated via pressure-volume integrals or above relations.
Isobaric Process
Definition
Pressure constant: P = const. Volume and temperature vary.
Heat and Work
Work done: W = PΔV. Heat: Q = nC_pΔT.
Internal Energy Change
ΔU = nC_vΔT. Difference Q−W equals ΔU.
Isochoric Process
Definition
Volume constant: V = const. No work done (W=0).
Heat Transfer
Heat added/removed changes internal energy: Q = ΔU = nC_vΔT.
Application
Heating in rigid containers, constant-volume calorimetry.
Cyclic Process
Definition
System returns to original state: ΔU = 0 over cycle.
Energy Balance
Net work output equals net heat input: W_net = Q_net.
Examples
Heat engines, refrigerators, Stirling cycles.
Work and Heat in Processes
Work Done by System
W = ∫ P dV. Positive if system expands, negative if compressed.
Heat Transfer
Q positive if heat absorbed, negative if released.
Sign Conventions
Consistent use vital: sign of W and Q depends on system perspective.
Examples Table
| Process Type | Heat (Q) | Work (W) | ΔU |
|---|---|---|---|
| Isothermal | Q = W | W ≠ 0 | 0 |
| Adiabatic | 0 | W = ΔU | ≠ 0 |
| Isobaric | Q ≠ 0 | W = PΔV | ≠ 0 |
| Isochoric | Q = ΔU | 0 | ≠ 0 |
First Law Applications
Statement
ΔU = Q − W. Internal energy change equals heat added minus work done by system.
Process Analysis
Calculate Q or W given ΔU and one other quantity. Enables energy accounting.
Example: Compression
Work done on gas increases U or transfers energy as heat depending on constraints.
Example: Expansion
Gas does work on surroundings; internal energy decreases unless compensated by heat input.
Process Diagrams
PV Diagram
Pressure vs volume. Area under curve = work done. Visualizes expansions, compressions.
TS Diagram
Temperature vs entropy. Useful for heat transfer visualization. Area under curve = heat.
Other Diagrams
PH diagram (pressure-enthalpy), UV diagram (internal energy-volume) for specialized analysis.
Example Table: Work Calculation
| Process | Work (W) | Diagram Area |
|---|---|---|
| Isothermal | W = nRT ln(V₂/V₁) | Area under PV curve |
| Isobaric | W = P(V₂−V₁) | Rectangle on PV diagram |
| Isochoric | 0 | Vertical line |
| Adiabatic | W = (P₂V₂ − P₁V₁)/(1−γ) | Curved PV line steeper than isothermal |
Limitations and Idealizations
Ideal Gas Assumption
Real gases deviate at high pressure/low temperature. Equations approximate behavior.
Quasi-Static Approximation
Processes assumed infinitely slow to maintain equilibrium. Real processes have irreversibilities.
No Phase Change
Most relations valid only if phase remains constant. Phase changes require latent heat considerations.
Neglect of Kinetic and Potential Energy
Often assumed negligible compared to internal energy; not true in some systems.
References
- Atkins, P.W., de Paula, J., Physical Chemistry, 10th ed., Oxford University Press, 2014, pp. 125-174.
- Moran, M.J., Shapiro, H.N., Fundamentals of Engineering Thermodynamics, 8th ed., Wiley, 2014, pp. 89-135.
- Cengel, Y.A., Boles, M.A., Thermodynamics: An Engineering Approach, 8th ed., McGraw-Hill, 2015, pp. 45-108.
- Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, 2nd ed., Wiley, 1985, pp. 200-255.
- Van Wylen, G.J., Sonntag, R.E., Fundamentals of Classical Thermodynamics, 2nd ed., Wiley, 1985, pp. 120-170.