General Concepts on Material Balance

Example 2. Unsteady-state condition. A tank initially contains 600 kg H2O and is fed with 100 kg/h H2O and has one stream going out at 80 kg/h. What is the mass balance for this system Is the system under steady state  

Learning the lesson of the first example, we will first define the system under analysis (dotted lines). 

System tank. Therefore, the mass balance in this case is 

Given that the right-hand-side term in (7.7) is equal to 20 (different from 0), we can state that the system (tank) is in an unsteady-state condition and, in addition, because the term is positive, the system is accumulating water at a ratio of 20 kg/h. As seen in Fig. 7.8, M(0) = 600, indicating that the mass in the tank at time 0 is 600 but, as was shown, is increasing at a ratio of 20 kg/h. 

Although simple, some steps are common and necessary in all material balance problems, (a) Graphically represent your process (tank and streams), (b) Define the system under analysis (here, the tank), (c) Define all the variables (input and output streams), (d) Formulate the material balance problem and solve it. 

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