First law of thermodynamics

First law of thermodynamics. It is a fundamental principle of physics stating that energy cannot be created or destroyed, only transformed from one form to another or transferred between systems. This law provides a rigorous formulation of the conservation of energy principle, incorporating heat as a form of energy transfer. It is a cornerstone for the fields of classical thermodynamics, engineering, and physical chemistry.

Statement of the law

The law asserts that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system minus the amount of work done by the system on its surroundings. This formulation explicitly links the concepts of heat, work, and internal energy. For any thermodynamic process, the net energy transfer is accounted for by these two mechanisms. A common paraphrase is that the total energy of an isolated system remains constant, a principle that extends back to the work of Julius Robert von Mayer. This statement invalidates the possibility of a perpetual motion machine of the first kind, which would produce work without an energy input.

Mathematical formulation

The differential form of the law is expressed as \( dU = \delta Q - \delta W \), where \( dU \) is the infinitesimal change in internal energy, \( \delta Q \) is the infinitesimal amount of heat added, and \( \delta W \) is the infinitesimal work done by the system. For a system where work is done by expansion against pressure, this becomes \( dU = \delta Q - p\,dV \). In the context of enthalpy \( H = U + pV \), the law transforms to \( dH = \delta Q + V\,dp \), which is particularly useful for analyzing constant-pressure processes in chemical engineering. The integrated form, \( \Delta U = Q - W \), is a direct expression of energy conservation applied over a finite process.

Applications and examples

This principle is applied ubiquitously in the analysis of heat engines, such as those described by the Carnot cycle, and in refrigeration cycles. In biochemistry, it governs energy transformations in processes like cellular respiration within mitochondria. The operation of internal combustion engines in automobiles and the design of steam turbines in power stations rely fundamentally on this energy accounting. Practical examples include the heating of a gas in a piston, where added heat increases internal energy and can perform work, and the Joule-Thomson effect, used in liquefaction of gases for applications like creating liquid nitrogen.

Historical development

The conceptual foundation was laid in the 19th century through the separate work of several scientists who recognized heat as a form of energy. Key figures include Julius Robert von Mayer, who proposed an early version of energy conservation in 1842, and James Prescott Joule, whose famous paddle-wheel experiment quantitatively demonstrated the equivalence of work and heat. Hermann von Helmholtz independently formulated a comprehensive theory of energy conservation in his 1847 work, *Über die Erhaltung der Kraft*. The formal integration of these ideas into thermodynamics is largely credited to Rudolf Clausius and Lord Kelvin, who established it as the first law within the thermodynamic framework.

Relation to other laws

It forms the foundational member of the four laws of thermodynamics. The second law of thermodynamics, introduced by Rudolf Clausius, introduces the concept of entropy and dictates the direction of spontaneous processes, complementing the energy accounting of the first law. The zeroth law of thermodynamics establishes the transitive property of thermal equilibrium, necessary for defining temperature, a key variable in applying the first law. The third law of thermodynamics, associated with Walther Nernst, concerns the behavior of entropy as temperature approaches absolute zero, a limit condition for energy transformations. Together, these laws govern all macroscopic energy interactions, from the Big Bang to biological systems.

Category:Thermodynamics Category:Conservation laws Category:Physics laws