Figure 1 shows a perfectly stirred tank with constant-volume. The two input streams, both consisting of the same liquid. The temperature and flow rate of each of the streams can vary with time. T Stream 1 T2 Stream 2 w2 T3 Stream 3 w3 Figure 1. Stirred tank with constant-volume 3.1. Derive a dynamic model that will describe transient operation. Make a degrees of freedom analysis assuming that both Streams 1 and 2 come from upstream units (i.e., their flow rates and temperatures are known functions of time). (7) 3.2. Simplify your model, if possible, to one or more differential equations by eliminating any algebraic equations. Also, simplify any derivatives of products of variables