materjalijäägi

Materjalijäägi, also known as mass balance, is a method used to track the flow of matter into and out of a defined system and to account for accumulation and chemical generation or consumption inside the system. It rests on the conservation of mass: mass cannot be created or destroyed within a closed system.

The overall mass balance for a control volume is dM/dt = sum_in ṁ_in − sum_out ṁ_out + ṁ_gen − ṁ_cons. At steady state, dM/dt = 0, so the input mass equals the output mass plus any net generation or consumption inside.

For each chemical species i, the balance is dN_i/dt = sum_in ṅ_i,in − sum_out ṅ_i,out + ν_i,gen − ν_i,cons. At steady state, sum_in ṅ_i,in = sum_out ṅ_i,out + net production/consumption of i. N_i is the amount of species i and ṅ_i are their flow rates. These balances can be written for all species in a mixture to determine compositions and rates.

Material balances apply to open systems and batch processes and are fundamental in reactor design, distillation, drying, mixing, and environmental accounting. They require consistent units and attention to phase changes and chemical reactions, since reactions change species composition while conserving total mass.

Example: a continuous stirred-tank reactor with feed flow F_in and outlet flow F_out at steady state has a total mass balance F_in = F_out. If a reaction A → B occurs with rate r, the component balances include −r for A and +r for B to predict outlet composition. Material balances are often used in conjunction with energy balances to model process performance.