Summary of Ideal Gas Laws

Thanks to ChatGPT for creating the table to my design. There's a long discussion with ChatGPT about the gas law equations here, where I revise my limited knowledge from school. (which was basically just understanding Boyle's Law and Charles's Law)

Law / Equation	Form / Equation	Derived From	Notes / Conditions
Boyle’s Law	P V = constant	Ideal Gas Law P V = n R T, with T = constant	Isothermal: pressure inversely proportional to volume
Charles’s Law	V / T = constant or V ∝ T	Ideal Gas Law P V = n R T, with P = constant	Isobaric: volume directly proportional to temperature
Gay-Lussac’s Law	P / T = constant or P ∝ T	Ideal Gas Law P V = n R T, with V = constant	Isochoric: pressure directly proportional to temperature
Ideal Gas Law	P V = n R T	Fundamental definition of ideal gases	Connects pressure, volume, temperature, and moles
Combined Gas Law	P V / T = constant P1 V1 / T1 = P2 V2 / T2	Ideal Gas Law, general form combining Boyle, Charles, Gay-Lussac	Relates pressure, volume, and temperature for a fixed amount of gas
Adiabatic PV Relation	P Vγ = constant	First Law dU = -P dV + Ideal Gas Law, γ = Cp/Cv	No heat transfer; pressure rises faster than 1/V
Adiabatic T–V Relation	T Vγ-1 = constant	PV adiabatic relation + Ideal Gas Law	Temperature rises when volume decreases (or vice versa)
Adiabatic T–P Relation	T = constant × P(γ-1)/γ	From PV and T–V adiabatic relations	Temperature as a function of pressure
Adiabatic PV Relation (states)	P1 V1γ = P2 V2γ	PV adiabatic relation applied to two states	Useful for calculating compression/expansion between two points
Adiabatic T–V Relation (states)	T1 V1γ-1 = T2 V2γ-1	T–V adiabatic relation applied to two states	Temperature change for volume change between two states
Adiabatic T–P Relation (states)	T2 = T1 (P2/P1)(γ-1)/γ	T–P adiabatic relation applied to two states	Temperature change for pressure change between two states