First Law

Overview

First Law of thermodynamics: energy conservation principle. Energy neither created nor destroyed. Total energy of isolated system constant. Energy transfer modes: work and heat. Core to physical chemistry: links microscopic molecular motion to macroscopic thermodynamic properties. Governs chemical reactions, phase transitions, and physical processes.

"Energy can be transformed from one form to another, but cannot be created or destroyed." -- Rudolf Clausius

Historical Background

Early Developments

18th-century heat studies. Caloric theory dominant. Count Rumford's cannon boring experiment (1798): mechanical work generates heat, refuting caloric theory.

Joule's Experiments

James Prescott Joule (1840s): mechanical equivalent of heat quantified. Demonstrated heat and work equivalence. Established energy conservation basis.

Formulation by Helmholtz and Mayer

Hermann von Helmholtz and Julius Robert Mayer independently formulated energy conservation principle for thermodynamics (1847–1850). Clarified energy transformations in physical systems.

Formulation and Mathematical Expression

Statement

Change in internal energy equals heat added to system minus work done by system:

ΔU = Q - W

Sign Conventions

Q > 0: heat absorbed by system. W > 0: work done by system on surroundings. Consistent sign usage critical.

Generalized Form

For infinitesimal changes:

dU = δQ - δW

Where dU is exact differential; δQ and δW are inexact differentials (path-dependent).

Internal Energy (U)

Definition

Sum of kinetic and potential energies of molecules in system. Includes translational, rotational, vibrational, electronic energies.

State Function

Depends solely on current thermodynamic state, independent of path. ΔU depends only on initial and final states.

Units and Measurement

SI units: joules (J). Absolute value inaccessible; changes measurable via calorimetry or indirect methods.

Work and Heat

Work (W)

Energy transfer via force acting through distance. Common form: pressure-volume work (expansion/compression). Calculated as:

W = ∫ P_ext dV

Heat (Q)

Energy transfer due to temperature difference. Mechanism: conduction, convection, radiation. Not a state function.

Comparison

Both are energy transfer methods, not contained within system. Measured indirectly through system property changes.

State Functions and Path Functions

State Functions

Properties depending only on current state: internal energy (U), enthalpy (H), entropy (S), pressure (P), volume (V), temperature (T).

Path Functions

Depend on transition path: work (W), heat (Q). Values vary with process route.

Implications

Only state function changes measurable directly; path functions inferred from state function differences and process conditions.

Enthalpy (H)

Definition

H = U + PV. Useful for processes at constant pressure.

Relation to First Law

At constant pressure, heat exchanged equals enthalpy change: Q_p = ΔH.

Applications

Calorimetry, reaction enthalpies, phase change studies.

Applications

Chemical Reactions

Determines energy changes. Predicts exothermic/endothermic nature. Basis for reaction energetics and equilibrium.

Phase Transitions

Energy required for melting, vaporization, sublimation quantified via enthalpy changes.

Calorimetry

Measurement of heat changes in chemical/physical processes. Validates first law experimentally.

Thermodynamic Cycles

Analysis of engines, refrigerators. Efficiency limits derived from energy conservation.

Experimental Verification

Joule's Paddle Wheel Experiment

Mechanical work converted to heat in water; verified mechanical equivalent of heat.

Calorimetric Measurements

Heat exchange measured under controlled conditions. Internal energy change inferred.

Modern Calorimeters

Bomb calorimeters, differential scanning calorimeters provide precise data supporting first law.

Limitations and Extensions

Limitations

Does not predict direction of processes (entropy required). Cannot determine spontaneity alone.

Extensions to Open Systems

First law adapted to account for mass flow, chemical reactions in open systems.

Relation to Second Law

Second law introduces entropy, irreversibility; complements energy conservation.

Related Concepts

Thermodynamic Potentials

Gibbs free energy (G), Helmholtz free energy (A) derived from first law and entropy considerations.

Heat Capacity

Defines relationship between heat added and temperature change. C_p and C_v distinctions.

Work Types

Expansion work, electrical work, surface work; all forms of energy transfer under first law framework.

Common Misconceptions

Heat as a Property

Heat is energy in transit, not stored in system. Misunderstanding leads to errors in thermodynamic analysis.

Work Always Positive

Work sign depends on process direction and convention; not inherently positive.

First Law Predicts Process Spontaneity

First law only conserves energy. Spontaneity determined by second law (entropy).

References

• Atkins, P., & de Paula, J. Physical Chemistry. Oxford University Press, 10th Ed., 2014, pp. 110-160.
• Callen, H.B. Thermodynamics and an Introduction to Thermostatistics. Wiley, 2nd Ed., 1985, pp. 45-80.
• Laidler, K.J., Meiser, J.H. Physical Chemistry. Benjamin-Cummings, 3rd Ed., 1982, pp. 200-230.
• Joule, J.P. "On the Mechanical Equivalent of Heat." Philosophical Transactions of the Royal Society, vol. 140, 1850, pp. 61-82.
• Clausius, R. "On the Motive Power of Heat." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 4, 1850, pp. 1-21.