Final answer:
In the provided equation, 'η' represents efficiency, which quantifies the conversion effectiveness of thermal energy to work. Thermal efficiency can also be expressed as Eff = (Qh - Qc) / Qh. Boyle's law and Amontons's/Gay-Lussac's law illustrate the relationships between pressure, volume, and temperature in thermodynamics.
Step-by-step explanation:
In the equation η = ((Q2-Q1)(P2+P1))/((P2-P1)(Q2+Q1)), the variable 'η' represents efficiency. Efficiency in thermodynamic processes is a measure of how well energy is converted from one form to another, typically from thermal energy into work or vice versa. The equation illustrates how the efficiency is influenced by heat transfer (represented by Q variables) and mechanical work (represented by P variables).
Regarding the mathematical expression of thermal efficiency, we can use the formulation Eff = (Qh - Qc) / Qh, where Qh is the heat added to the system and Qc is the heat released or transferred out of the system. This shows that perfect efficiency of 1, or 100%, is only achievable if there is no heat transfer to the environment (Qc = 0).
Pressure and volume have an important relationship in thermodynamics as described by Boyle's law, which states that at constant temperature, the product of pressure and volume for a given sample of gas remains constant (P1V1 = P2V2). Additionally, in the context of Amontons's/Gay-Lussac's law, we see direct proportionality between pressure and temperature when volume is kept constant.