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Part of THERM-01 — Thermodynamics & Kinetic Theory of Gases

Visual Overview: PV Diagrams, Process Tables, and Gas Property Reference

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P-V Diagram — Four Processes Starting from the Same State

V P ($P_{1}$,$V_{1}$,$T_{1}$) Isobaric P=const Isothermal PV=k Adiabatic PV^γ=k Isochoric V=const Area under curve = Work (W) Adiabatic steeper than Isothermal (γ > 1)

Process Comparison Table

Process	Constant	Q	W	$\Delta U$	PV Curve
Isothermal	T	nRT ln( $V_{2}$ / $V_{1}$ )	nRT ln( $V_{2}$ / $V_{1}$ )	0	Hyperbola
Adiabatic	Q = 0	0	nCᵥ( $T_{1}$ − $T_{2}$ )	nCᵥ( $T_{2}$ − $T_{1}$ )	Steeper hyperbola
Isochoric	V	nCᵥ $\Delta T$	0	nCᵥ $\Delta T$	Vertical line
Isobaric	P	nCₚ $\Delta T$	nR $\Delta T$	nCᵥ $\Delta T$	Horizontal line

Gas Properties Table

Gas Type	Examples	f	Cᵥ	Cₚ	γ
Monoatomic	He, Ne, Ar	3	3R/2	5R/2	5/3 = 1.67
Diatomic	$H_{2}$ , $O_{2}$ , $N_{2}$	5	5R/2	7R/2	7/5 = 1.40
Polyatomic	C $O_{2}$ , $H_{2}$ O	6	3R	4R	4/3 = 1.33

Molecular Speed Reference

Speed	Formula	Value for $O_{2}$ at 300 K	Ratio
v_mp	√(2RT/M)	394.8 m/s	1.000
v_avg	√(8RT/πM)	445.5 m/s	1.128
v_rms	√(3RT/M)	483.6 m/s	1.224

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