2.4
Función de estado, diferenciales exactos e inexactos
Una función de estado es una propiedad termodinámica que depende únicamente del estado actual de un sistema, independientemente de su historia o de có…
Consideremos un sistema que experimenta una expansión adiabática desde un estado inicial con cierta energía interna hasta un estado final con una energía interna diferente. Aquí, el trabajo realizado por el sistema se denota como w.
Si el proceso cambia a no adiabático manteniendo los mismos estados inicial y final, el cambio en la energía interna permanece igual. Sin embargo, el calor y el trabajo difieren entre los caminos, lo que refleja que la energía interna es independiente del camino, mientras que el trabajo y el calor dependen del camino.
Propiedades como la energía interna que dependen únicamente del estado actual del sistema se denominan funciones de estado.
Por otro lado, las cantidades físicas dependientes del camino, como el trabajo y el calor, se denominan funciones de camino.
Las funciones de estado y camino se simbolizan con letras mayúsculas y minúsculas, respectivamente.
Los cambios infinitesimales en la obra, el calor y la energía interna se representan por diferenciales δw, δq y dU.
Cuando se integran, δw y δq indican la cantidad absoluta de trabajo y calor involucrados en el proceso, categorizándolos como diferenciales inexactos, mientras que dU da el cambio en U, marcándolo como un diferencial exacto.
View the full transcript and gain access to JoVE Core videos
Q1: What is a state function in thermodynamics?
A state function is a thermodynamic property that depends solely on the system's current state, not on how it arrived there. Examples include internal energy (U), enthalpy (H), and entropy (S), represented by capital letters. Whether a system follows a linear or complex path, its state function values remain identical at the same initial and final conditions.
Q2: How do path functions differ from state functions?
Path functions depend on the specific route a system takes between states, while state functions do not. Work (w) and heat (q) are path functions, represented by lowercase letters, and their values vary depending on the process pathway. In contrast, state functions like internal energy remain constant regardless of the path taken.
Q3: What is the difference between exact and inexact differentials?
Exact differentials, like dU for internal energy, integrate to give path-independent values. Inexact differentials, like δw and δq for work and heat, integrate to give path-dependent values. When integrated, dU yields the change in internal energy (ΔU), while δw and δq yield absolute amounts of work and heat that depend on the process path.
Q4: Why does internal energy remain unchanged when a process changes from adiabatic to nonadiabatic?
Internal energy is a state function, depending only on initial and final states, not the process type. When a system transitions from adiabatic to nonadiabatic expansion while maintaining the same starting and ending states, the change in internal energy stays identical. However, the individual values of heat and work redistribute between the two paths.
Q5: What does the cyclic integral of a state function equal?
For a cyclic process where the system returns to its initial state, the cyclic integral of any state function equals zero. This reflects the path-independent nature of state functions. Conversely, cyclic integrals of path functions like heat and work are not necessarily zero, since these quantities depend on the specific process pathway.
Q6: Why are state functions represented by capital letters and path functions by lowercase letters?
This notation convention distinguishes between two fundamental thermodynamic property types. Capital letters (U, H, S) denote state functions that depend only on system state. Lowercase letters (w, q) denote path functions whose values depend on the process route. This symbolic distinction helps clarify whether a quantity is path-independent or path-dependent.
Q7: How do infinitesimal changes in work, heat, and internal energy differ mathematically?
Infinitesimal changes are represented as δw, δq, and dU respectively. The δ symbol denotes inexact differentials for work and heat, indicating path-dependence. The d symbol denotes the exact differential for internal energy, indicating path-independence. When integrated, δw and δq yield absolute amounts dependent on the process, while dU yields the change in internal energy independent of path.