PHY.6:4.2 - Construct the balances with physical meanings

Use C.29.BB to choose the additive quantity, common interval, signs, transfers and internal production. Write each term with its physical meaning and compatible units. For vector quantities, use a common frame or an explicit transformation between frames.

For a fixed spatial region, a useful form is

rate of stored quantity = inward transfer - outward transfer + internal production.

A local continuity equation expresses the same relation for a density and its flux. The choice of quantity determines the production term: a chemical species can be consumed while the atoms it contains remain in reaction products. A closed boundary alone does not make every selected quantity constant.

Identify which terms remain undetermined. A momentum balance may still need forces; a species balance may need transport and reaction rates. If the requested total already follows without those details, retain that consequence and avoid completing an unnecessary model.