A toy per-particle thermal energy becomes a checked total. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Particle count multiplies toy thermal energy

There are 6 particles, each with 2 joules of toy thermal energy.

626\cdot2
Osmotic pressure ledgerParticle thermal energy closes the pressure-volume budget.thermalvolumepressurepV

Thermal energy total is checked

The total thermal energy is 12 joules.

62=126\cdot2=12
Osmotic pressure ledgerParticle thermal energy closes the pressure-volume budget.thermalvolumepressurepV