# Mass Balance for Open Systems

Change in the Total
Mass of the System
=
Total Mass of the
System at Final State
-
Total Mass of the
System at Initial State
Differential Mass Balance :
Change in the Total
Mass of the System
Total Mass
Leaving the System
Total Mass
Entering the System
=
-
Integral Mass Balance :
Open
System

## Conservation of Mass Principle (or Mass Balance)

Mass cannot be created or destroyed. Therefore, as we did for energy, we must account for all mass flows that cross the system boundary.
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### Ch 5, Lesson A, Page 2 - Mass Balance for Open Systems

• A mass balance equation basically says that if mass enters the system, it either leaves or it accumulates within the system.
• IN – OUT = ACCUMULATION
• In an integral mass balance, IN and OUT must be amounts, such as 26 kg of carbon dioxide.
• In a differential material balance, IN and OUT are mass flow rates, such as 4.4 kg oxygen per sec.
• But, what about the accumulation terms in these material balance equations ?
• Well, in an integral material balance, the accumulation term is just the AMOUNT of mass that accumulates inside the system during the process.
• We use the symbol Dmsys for the accumulation term because it is the final mass of the system minus the initial mass of the system.  So, Dmsys is indeed the change in the mass of the system and that is exactly what accumulation means in an integral material balance equation.
• In a differential material balance, the accumulation term is the TIME RATE OF CHANGE of the mass within the system boundary.
• Check the units in the differential mass balance equation to make sure you feel confident about this equation.
• The mass flow rate terms have units of mass per time, like kg/h.
• The units of d/dt are inverse time or per hour.  The units for msys are just kg.  So, the units for the accumulation term work out to be kg/h and our differential mass balance is, indeed, dimensionally homogeneous.
• That isn’t too bad, right ?
• What if we have more than one inlet or outlet stream ?  What symbols do we use for all of the flow rates ?
• Flip the page and let’s see.