Law of Conservation of Mass: Mass can neither be created nor destroyed (except in nuclear reactions).
Because of this, we can write equations called "mass balances" or "material balances". Any process being studied must satisfy balances on the total amount of material, on each chemical component, and on individual atomic species. Later in the course, we'll use the Law of Conservation of Energy (1st Law of Thermodynamics) to write similar balance equations for energy.
(Applies to mass, components, energy, etc.)
The system is any process or portion of a process chosen by the engineer for analysis. A system is said to be "open" if material flows across the system boundary during the interval of time being studied; "closed" if there are no flows in or out.
Accumulation is usually the rate of change of holdup within the system -- the change of material within the system. It may be positive (material is increasing), negative (material decreasing), or zero (steady state).
If the system does not change with time, it is said to be at steady state, and the net accumulation will be zero.
For our purposes, the generation and consumption terms are the consequence of chemical reaction. Note that while the total mass of a system and elements (or "atoms") are conserved, individual species are not.
If there is no chemical reaction, the production and consumption terms are typically zero.
Your bank statement can be thought of as a "dollar balance". Specifically, an "integral form balance" on dollars.
All the terms are rates, so the balance describes an instant in time. Usually the best choice for a continuous process. When formulated for an instant in time, the result is an ordinary differential equation. This is what we used on steady flow systems in Thermo I.
(Also called cumulative form) Written using total amounts as terms, so it describes the overall effect. Often a good choice for batch processes. In Thermo I, we used these on both closed and uniform state problems.
In this class, most problems will be differential balances on steady state systems. Consequently, accumulation will usually be zero.
The flow terms can usually be easily identified from the problem statement. If the process is batch, these may be zero.
Production and consumption are almost never present when balancing total mass, and are only present in component balances when reaction occurs.
The figure describes a mixing tank problem. Find all flows and compositions.
Start with the general balance equation:
If we assume the system is at steady state (and there is no indication not to), accumulation is zero, and:
Now we need to figure out the composition of the product stream. Start with the general equation and write a component balance on compound A:
Similar balances are done on compounds B and C:
It is always smart to check answers for consistency. Here, we do this by summing the mole fractions:
In the example, we wrote and solved one total material balance and three component balances, for a total of four balance equations describing a three component system. Is this the right number?
Try, whenever possible, to write the easy balance equations! In the example, this might have lead to the sequence:
Balances can also be written on atoms -- which like total mass, are always conserved. These "atom balances" are useful in certain classes of balance problems where reaction is present.
Consider the complete combustion of methane:
You could write a component balance on methane (assuming steady state):
To review, solving a problem goes like this:
WARNING: Mass and atoms are conserved. Moles are conserved only when there is no reaction. Volume is NOT conserved.
You may write balances on total mass, total moles, mass of a compound, moles of an atomic species, moles of a compound, mass of a species, etc.
Modified: 9/12/94, 9/4/96, 9/8/98; 12/25/2004
Copyright 1996, 1998, 2004 by R.M. Price -- All Rights Reserved