Osmotic pressure is taught as exact pressure-volume energy closure. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Pressure times volume is energy

Pressure 4 pascals over volume 3 cubic metres gives 12 joules.

43=124\cdot3=12
Osmotic pressure ledgerParticle thermal energy closes the pressure-volume budget.thermalvolumepressurepV

pV equals the particle energy ledger

The pressure-volume value 12 matches the thermal total 12.

12=12 J12=12\ \text{J}
Osmotic pressure ledgerParticle thermal energy closes the pressure-volume budget.thermalvolumepressurepV