# ChE: Define the term balance equation and give examples of things that might be balanced

### Balance Equations

Imagine the following:

• the US mints all close, so that no new \\$1 bills are ever generated
• none of the bills ever wears out

If these two things held true, the total number of \\$1 bills in the world would never change. That is, they would be conserved.

DEFINITION

If something is conserved, the total number (or amount) never changes.

If \\$1 were conserved, then you could easily keep track of how many where in your wallet (or bank account) by simply comparing how much comes in versus how much comes out (we will ignore interest for now).

If both IN and OUT were the same number (or the same rate (for example, dollars per hour)), then the total amount of money in your account would always be the same. If IN is bigger than out, you are accumulating dollars; if OUT is bigger you are depleting your supply (which we will call a negative accumulation).

What we have just done is a simple balance on dollars, using the following balance equation:

ACCUMULATION = IN - OUT

DEFINITION

A balance equation is a tool used to account for where things come/go and how their total number (or amount) changes.

If we now consider interest, it is possible for the total amount in your account to increase without you putting any money in yourself. We will call this generation, similarly the bank might change you something for having an account (so the total amount decreases without your taking any out), so that some is consumed.

A more general balance equation then, is given as

ACCUMULATION = IN - OUT + GENERATION - CONSUMPTION

OUTCOME:

Define the term balance equation and give examples of things that might be balanced

NOTE:

A balance need not be done only on conserved quantities.

NOTE:

In fact, if a material is truly conserved generation and consumption must both be zero. In other words, a balance on total dollars in this example could not have generation and consumption. Our example did involve generation and consumption because we were doing a specific balance on your money (not total money) so you "generated" dollars by taking them from someone else and "consumed" them by giving them to someone else.