Graph 1: P vs V (Boyle's Law) Shape: Hyperbola. Each temperature gives a different hyperbola (isotherm). Higher T isotherms are further from origin. PV = constant along any isotherm. Image: https://commons.wikimedia.org/wiki/Special:FilePath/Boyles_Law_animated.gif?width=600
Graph 2: V vs T (Charles's Law) Shape: Straight line with positive slope. Extrapolates to V = 0 at T = 0 K (-273.15°C). Different pressures give parallel lines. Image: https://commons.wikimedia.org/wiki/Special:FilePath/Charles_and_Gay-Lussac_Law_animated_2.gif?width=600
Graph 3: Z vs P (Compressibility factor)
- Ideal gas: horizontal line at Z = 1
- at low T: dips below 1 (attraction), then rises above 1 (repulsion)
- and He: always above Z = 1 at all pressures
- All gases converge to Z = 1 as P → 0 Image: https://commons.wikimedia.org/wiki/Special:FilePath/Compressibility_factor_for_various_gases.png?width=600
Graph 4: Maxwell-Boltzmann Speed Distribution Shape: asymmetric bell curve. Peak = v_mp. Mean = v_avg (slightly right of peak). RMS = v_rms (further right). At higher T: peak shifts right and flattens (broader distribution, lower peak). Total area constant. Image: https://commons.wikimedia.org/wiki/Special:FilePath/Maxwell-Boltzmann_distribution_1.svg?width=600
Graph 5: Andrews Isotherms for Below T_c (31.1°C): horizontal plateau (gas-liquid coexistence) at each T. At T_c: inflection point (critical isotherm) — no horizontal portion. Above T_c: smooth curve — supercritical fluid. Image: https://commons.wikimedia.org/wiki/Special:FilePath/Andrews_isotherm_of_CO2.svg?width=600