First Law and Energy Conservation

The first law of thermodynamics extends the conservation of energy to thermal processes, identifying heat and work as interchangeable ways of changing a system's internal energy.

Definition

The first law of thermodynamics states that the change in a system's internal energy equals the heat added to the system minus the work done by it, expressing the conservation of energy when heat is included as a form of energy transfer.

Scope

This topic covers the statement of the first law, the internal energy as a state function, the path-dependence of heat and work, exact and inexact differentials, and the formulation dU = dQ - dW. Applications to enthalpy, heat capacities, and the analysis of thermodynamic processes such as isothermal, adiabatic, and isochoric paths are included.

Core questions

• Why is internal energy a state function while heat and work are not?
• How did the mechanical equivalent of heat establish energy conservation across thermal and mechanical domains?
• How do heat and work combine to determine energy changes along different process paths?
• What distinguishes enthalpy from internal energy and when is each natural to use?

Key concepts

• Internal energy as a state function
• Heat and work as path-dependent transfers
• Exact versus inexact differentials
• Enthalpy and heat capacities
• Adiabatic, isothermal, and isochoric processes

Clinical relevance

The first law underlies energy accounting in engines, calorimetry, chemical reaction enthalpies, and metabolic energy balance, providing the bookkeeping principle for every process that exchanges heat and work.

History

The first law crystallized in the 1840s as Mayer and Joule independently established the mechanical equivalent of heat and Helmholtz argued for the universal conservation of energy, unifying mechanics, heat, and other forms of energy.

Key figures

• James Prescott Joule
• Julius Robert von Mayer
• Hermann von Helmholtz

Seminal works

• joule1850
• callen1985

Frequently asked questions

Why are heat and work written with inexact differentials?

Because the heat exchanged and work performed depend on the path taken between two states, not just the endpoints, whereas internal energy depends only on the state; the inexact differential notation marks this path dependence.