Gas and Engine Relation Scans

Boyle Three-State Scan

inverse pressure-volume pairs

Three exact pressure-volume rows make fixed-temperature inverse scaling readable. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Low pressure pairs with large volume

At fixed kelvin temperature, pressure 2 pascals pairs with volume 6 cubic metres so the product is 12 joules.

pV=2 Pa⋅6 m3=12 JpV=2\ \text{Pa}\cdot6\ \text{m}^{3}=12\ \text{J}
Boyle scanThe outer rows are shown as checked piston states.6 m^32 Pa 300 Kstate3 m^34 Pa 300 Kstate

Middle pressure keeps the same product

The middle row uses pressure 3 pascals and volume 4 cubic metres. The product stays 12 joules.

pV=3 Pa⋅4 m3=12 JpV=3\ \text{Pa}\cdot4\ \text{m}^{3}=12\ \text{J}

High pressure pairs with small volume

The third row raises pressure to 4 pascals and lowers volume to 3 cubic metres. Three rows make the inverse pair visible.

pVpV2 Pa6 m312 J3 Pa4 m312 J4 Pa3 m312 J\begin{array}{c|c|c}p&V&pV\\2\ \text{Pa}&6\ \text{m}^{3}&12\ \text{J}\\3\ \text{Pa}&4\ \text{m}^{3}&12\ \text{J}\\4\ \text{Pa}&3\ \text{m}^{3}&12\ \text{J}\\\end{array}
Boyle scanThe table and checked piston diagram keep pV equal.6 m^32 Pa 300 Kstate3 m^34 Pa 300 Kstate