Definition of Work
General Concept
Work: energy transfer caused by a force acting through a displacement. Unit: joule (J). Scalar quantity. Path-dependent process function.
Physics vs Thermodynamics
Physics: work = force × distance. Thermodynamics: work = energy crossing system boundary excluding heat transfer.
System and Surroundings
Work done by system on surroundings: energy leaves system. Work done on system by surroundings: energy enters system. Boundary: interface where work crosses.
Work in Thermodynamics
Energy Transfer Mode
Work: one of two modes of energy transfer (other: heat). Non-random, organized energy transfer. Affects internal energy of system.
Process Dependent
Work depends on process path, not just initial and final states. Non-state function.
Work and State Functions
Work not a state function; internal energy and enthalpy are state functions influenced by work and heat.
Types of Work
Pressure-Volume Work
Work due to volume change against external pressure. Most common in gases.
Electrical Work
Energy transfer via electrical current flow. Example: electrochemical cells.
Other Mechanical Work
Examples: shaft work, moving pistons, stirring, surface tension work.
Pressure-Volume Work
Definition
Work done when system volume changes against external pressure: W = -P_ext ΔV.
Expansion and Compression
Expansion: system does work on surroundings (W < 0). Compression: surroundings do work on system (W > 0).
Quasi-Static Processes
Assumes infinitesimal changes maintaining equilibrium. Enables calculation of reversible work.
Work Equations
General Expression
Infinitesimal work: dW = -P_ext dV (pressure-volume work). Negative sign per sign convention.
Integral Form
W = - ∫ P_ext dVReversible Work
W_rev = - ∫ P dVP: system pressure, equals external pressure for reversible process.
Sign Convention
Work Done by System
Work done by system on surroundings: negative value (energy leaves system).
Work Done on System
Work done on system by surroundings: positive value (energy enters system).
Consistency
Sign convention ensures consistent application in first law calculations.
| Process | Work Sign | Interpretation |
|---|---|---|
| Expansion | Negative | System does work on surroundings |
| Compression | Positive | Surroundings do work on system |
Reversible vs Irreversible Work
Reversible Work
Idealized process: infinitely slow, quasi-static. System always near equilibrium. Maximum work extraction.
Irreversible Work
Real processes: finite speed, dissipative effects. Less work done compared to reversible case.
Work Comparison
Magnitude: |W_irrev| < |W_rev| for expansion; work lost due to friction, turbulence, gradients.
Work and the First Law of Thermodynamics
First Law Statement
ΔU = Q - W; internal energy change equals heat added minus work done by system.
Work as Energy Transfer
Work and heat: energy crossing boundary. Work reduces internal energy if done by system.
Closed vs Open Systems
In closed systems: work mainly pressure-volume work. Open systems: additional forms like shaft work.
Work Calculation Methods
Graphical Integration
Work equals area under pressure-volume curve. Useful for quasi-static processes.
Analytical Integration
Apply equations for ideal gases, polytropic processes, isothermal, adiabatic expansions.
Numerical Methods
Discrete data integration for experimental or simulated data sets.
| Process Type | Work Formula | Remarks |
|---|---|---|
| Isothermal Expansion (Ideal Gas) | W = -nRT ln(V2/V1) | Temperature constant, reversible |
| Adiabatic Expansion | W = (P2V2 - P1V1)/(γ - 1) | No heat transfer, γ = Cp/Cv |
Examples of Work in Thermodynamics
Gas Expansion in Piston
Gas expands, pushing piston upward. Work done against external pressure. Energy leaves system.
Stirring Work
Mechanical stirring transfers energy into fluid. Work done on system increases internal energy.
Electrical Work in Electrochemical Cells
Electrons flow through external circuit; work done by system depends on cell potential and current.
Limitations and Assumptions
Quasi-Static Approximation
Calculations often assume slow processes to maintain equilibrium; real processes deviate.
Ideal Gas Assumption
Many work formulae assume ideal gas behavior; deviations at high pressure, low temperature.
Neglect of Non-PV Work
Pressure-volume work dominates in many cases; other work forms may be significant in some systems.
References
- Atkins, P.W., Physical Chemistry, 10th ed., Oxford University Press, 2014, pp. 200-230.
- Smith, J.M., Van Ness, H.C., Abbott, M.M., Introduction to Chemical Engineering Thermodynamics, 7th ed., McGraw-Hill, 2005, pp. 120-150.
- Çengel, Y.A., Boles, M.A., Thermodynamics: An Engineering Approach, 8th ed., McGraw-Hill, 2015, pp. 75-110.
- Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, 2nd ed., Wiley, 1985, pp. 50-90.
- Reid, R.C., Prausnitz, J.M., Poling, B.E., The Properties of Gases and Liquids, 4th ed., McGraw-Hill, 1987, pp. 45-80.