تسجيل الدخول

تسجيل

Properties of the internal energy

المؤلف:  Peter Atkins، Julio de Paula

المصدر:  ATKINS PHYSICAL CHEMISTRY

الجزء والصفحة:  103

2025-11-09

492

Properties of the internal energy

Equation 3.43 shows that the internal energy of a closed system changes in a simple way when either S or V is changed (dU∝dS and dU∝dV). These simple proportionalities suggest that U should be regarded as a function of S and V. We could regard U as a function of other variables, such as S and por TandV, because they are all interrelated; but the simplicity of the fundamental equation suggests that U(S,V) is the best choice. The mathematical consequence of U being a function of S and Vis that we can express an infinitesimal change dU in terms of changes dS and dV by

The two partial derivatives are the slopes of the plots of U against S and V, respectively. When this expression is compared to the thermodynamic relation, eqn 3.43, we see that, for systems of constant composition,

The first of these two equations is a purely thermodynamic definition of temperature (a Zeroth-Law concept) as the ratio of the changes in the internal energy (a First-Law concept) and entropy (a Second-Law concept) of a constant-volume, closed, constant composition system. We are beginning to generate relations between the properties of a system and to discover the power of thermodynamics for establishing unexpected relations.