Introduction
First Law Formulation: expresses energy conservation for thermodynamic systems. Establishes relation between heat added, work done, and internal energy change. Foundation of classical thermodynamics. Applies universally: engines, refrigerators, biological systems, chemical reactions.
"Energy can neither be created nor destroyed; it can only be transformed from one form to another." -- Rudolf Clausius
Historical Background
Development of Energy Concepts
18th-century debates: caloric theory vs mechanical energy. James Joule's experiments linking heat and mechanical work. Hermann von Helmholtz's conservation of energy principle. Rudolf Clausius and William Thomson formalized thermodynamic laws.
Formulation of the First Law
Joule’s paddle-wheel experiment quantified mechanical equivalent of heat. Clausius introduced internal energy concept. Kelvin stated energy conservation in cyclic processes. Planck and Carathéodory refined mathematical rigor.
Impact on Science and Engineering
Enabled design of heat engines, refrigerators. Advanced understanding of chemical thermodynamics. Established quantitative energy accounting framework. Precursor to second law and entropy concepts.
Definition and Statement
Qualitative Statement
Energy of an isolated system is constant. Energy transfer occurs as heat or work. Internal energy changes reflect net energy exchanges.
Quantitative Statement
Change in internal energy equals heat added minus work done by system.
Formal Expression
ΔU = Q - W
ΔU = Q - Wwhere,ΔU = change in internal energy,Q = heat added to the system,W = work done by the systemKey Concepts
Energy Conservation
Energy cannot be created or destroyed. Total energy in system and surroundings conserved.
Internal Energy (U)
Sum of microscopic kinetic and potential energies of particles. State function, depends only on current state.
Heat (Q)
Energy transfer due to temperature difference. Positive when added to system.
Work (W)
Energy transfer due to force acting through displacement. Positive when system does work on surroundings.
State Functions vs Path Functions
Internal energy: state function (depends on state only). Heat and work: path functions (depend on process).
Mathematical Formulation
General Energy Balance
For closed systems:
dU = δQ - δW(U differential change; δQ heat increment; δW work increment)Work Types
Boundary work: W = ∫P dV (pressure-volume work). Shaft work, electrical work also relevant.
Heat Transfer Modes
Conduction, convection, radiation. Heat transfer rate Q̇ often time-dependent.
Cyclic Process
System returns to initial state: ΔU = 0; thus Q = W.
Energy Balance for Open Systems
Includes mass flow: ΔE = Q - W + m_in h_in - m_out h_out (h = enthalpy).
Types of Thermodynamic Systems
Isolated System
No mass or energy exchange with surroundings. ΔU = 0.
Closed System
Mass fixed; energy transfer via heat and work allowed.
Open System
Mass and energy exchange allowed. Control volumes like turbines, compressors.
Quasi-Static Process
System remains near equilibrium during process. Enables precise energy calculations.
Steady-State vs Transient
Steady-state: properties constant in time. Transient: properties vary with time.
Energy Interactions: Heat and Work
Heat Transfer (Q)
Driven by temperature gradient. Units: Joules (J), calories.
Work (W)
Mechanical work: pressure-volume, shaft work. Electrical work: current flow.
Sign Convention
Positive Q: heat into system. Positive W: work done by system.
Boundary Work
Work due to volume change under pressure: W = ∫P dV.
Non-PV Work
Includes electrical, magnetic, surface tension work.
Internal Energy
Definition
Total microscopic energy: translational, rotational, vibrational, electronic.
State Function Properties
Depends only on state variables: pressure, temperature, volume.
Relation with Enthalpy
H = U + PV; useful in open system analysis.
Measurement
Determined via calorimetry and indirect calculations.
Changes in Internal Energy
Result of heat addition or work done on/by system.
| Property | Description |
|---|---|
| Internal Energy (U) | Microscopic kinetic + potential energy of molecules |
| Enthalpy (H) | U + PV, useful in flow processes |
| Heat (Q) | Energy transfer due to temperature difference |
| Work (W) | Energy transfer due to force-displacement |
Applications and Examples
Heat Engines
Convert heat into work via cyclic processes. Efficiency limited by first and second laws.
Refrigerators and Heat Pumps
Use work input to transfer heat from cold to hot reservoirs.
Chemical Reactions
Energy balance accounts for enthalpy changes, reaction heat.
Biological Systems
Metabolic energy transformations obey first law.
Industrial Processes
Design of boilers, turbines, compressors depends on energy conservation.
Limitations and Extensions
Does Not Predict Direction
First law quantifies energy but not spontaneity or irreversibility.
Combined with Second Law
Second law introduces entropy, determines process feasibility.
Non-Classical Systems
Quantum, relativistic effects require advanced formulations.
Open Systems Complexity
Mass and energy flows complicate energy accounting.
Thermodynamic Potentials
Extensions include Helmholtz and Gibbs free energies for equilibrium analysis.
Example Problems
Closed System with Boundary Work
Calculate ΔU when 500 J heat added, 300 J work done by system.
Given:Q = +500 JW = 300 J (work done by system)ΔU = Q - W = 500 - 300 = 200 JIsothermal Expansion of Ideal Gas
Work done during isothermal expansion: W = nRT ln(V2/V1)
Steady Flow Energy Equation
For turbine: W = m (h1 - h2)
Energy Balance in Mixing Process
Sum of enthalpies before and after mixing equals zero for adiabatic system.
Heat Engine Efficiency
η = W_net / Q_in; first law limits maximum work output.
| Problem | Solution Outline |
|---|---|
| Closed system energy change | Use ΔU = Q - W; substitute known values |
| Isothermal gas expansion work | Calculate using ideal gas law and logarithmic volume change |
| Turbine energy balance | Apply steady flow equation with enthalpy differences |
Summary
First law: fundamental energy conservation principle in thermodynamics. Relates heat, work, and internal energy changes. Applies to all system types and processes. Foundation for engineering design and scientific analysis. Limitations addressed by second law and advanced thermodynamics.
References
- Çengel, Y.A., Boles, M.A., "Thermodynamics: An Engineering Approach," McGraw-Hill, Vol. 7, 2015, pp. 1-850.
- Moran, M.J., Shapiro, H.N., "Fundamentals of Engineering Thermodynamics," Wiley, 8th ed., 2014, pp. 45-670.
- Gaskell, D.R., "Introduction to the Thermodynamics of Materials," Taylor & Francis, 5th ed., 2008, pp. 100-400.
- Van Wylen, G.J., Sonntag, R.E., Borgnakke, C., "Fundamentals of Classical Thermodynamics," Wiley, 7th ed., 2012, pp. 50-550.
- Atkins, P., de Paula, J., "Physical Chemistry," Oxford University Press, 10th ed., 2014, pp. 200-600.