A stirred tank contains 1500 lbm of pure water at 70F. At time t 0, two streams begin to

Chapter 10, Problem 10.15

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A stirred tank contains 1500 lbm of pure water at 70F. At time t 0, two streams begin to flow into the tank and one is withdrawn. One input stream is a 20.0 wt% aqueous solution of NaCl at 85F flowing at a rate of 15 lbm/min, and the other is pure water at 70F flowing at 10 lbm/min. The mass of liquid in the tank is held constant at 1500 lbm. Perfect mixing in the tank may be assumed, so that the outlet stream has the same NaCl mass fraction (x) and temperature (T) as the tank contents. Also assume that the heat of mixing is zero and the heat capacity of all fluids is Cp = 1 Btu/(lbmF). (a) Write differential material and energy balances and use them to derive expressions for dx=dt and dT=dt. (b) Without solving the equations derived in Part (a), sketch plots of T and x as a function of time (t). Clearly identify values at time zero and as t ! 1.