In mathematics, "z", lower case, is the symbol for the vertical axis in the Cartesian coordinate system.
In 1875, Rudolf Clausius employed upper “Z” and lower case “z” in his derivation of the forces involved in the work function of a moving body: 
- “W is the work done whenever a body moves under the influence of a force. The product of the force and distance moved through is the mechanical work which the force performs during the motion.”
- — Rudolf Clausius (1875), The Mechanical Theory of Heat (§: Mathematical Introduction)
In 1924, James Partington, was employing the symbol "Z" thusly: “Z is called the thermodynamic potential by analogy with the potential function in dynamics: ϕ1 – ϕ2 = work”, was employed as the symbol for the isothermal-isobaric thermodynamics potential: 
In other words, Z, at one point was a symbol for the Gibbs energy, in modern parlance. 
The letter “Z” is also sometimes employed as the “compressibility factory” of a gas (see: characteristic function notation table). 
1. Thims, Libb. (2020). Human Chemical Thermodynamics — Chemical Thermodynamics Applied to the Humanities: Meaning, Morality, Purpose; Sociology, Economics, Ecology; History, Philosophy, Government, Anthropology, Politics, Business, Jurisprudence; Religion, Relationships, Warfare, and Love (§2: Alphabet) (pdf). Publisher.
2. (a) Symbols (EoHT.info) -- Hmolpedia 2020.
(b) Symbols – EoHT.info | Internet Archive (21 Feb 2020).
3. Partington, James. (1924). Chemical Thermodynamics: An Introduction to General Thermodynamics and its Applications to Chemistry. D. Van Nostrand.
4. Compressibility factor – Wikipedia.
- Z – Wikipedia.