Thermodynamics, First Law of

one of two basic laws of thermodynamics. It is a law of the conservation of energy in systems in which thermal processes are of significant importance. The law was formulated in the mid-19th century as a result of the work of J. R. Mayer, J. Joule, and H. Helmholtz. It states that a thermodynamic system, for example, steam in a heat engine, can perform work only at the expense of its internal energy or of an external source of energy. The law is frequently formulated as the impossibility of a perpetual-motion machine of the first kind, a machine that would perform work without consuming energy.

When a certain quantity of heat Q is imparted to a thermodynamic system, there in general occurs a change ΔU in the internal energy of the system and the system performs the work A:

(1) Q = ΔU + A

Equation (1), which expresses the first law of thermodynamics, is also a definition of the change ΔU of the internal energy of the system, since Q and A are independently measurable quantities.

The internal energy U of the system can, in particular, be determined by measuring the work of the system in an adiabatic process, that is, when Q= 0: A_ad = —Δ U. Thus we can determine U to within an accuracy of an additive constant U₀:

(2) U = δU + U₀

The first law of thermodynamics maintains that U is a function of the state of the system; that is, each state of the thermodynamic system is characterized by a specific value of U, regardless of the path by which the system attained that state. In contrast, Q and A depend on the process that causes the change of the state of the system. The first law of thermodynamics is usually applied jointly with the second law of thermodynamics in studies of the thermodynamic properties of systems.