A stirred tank contains 1500 lb_m of pure water at 70°F. At time t = 0, two streams begin to flow into the tank and one is withdrawn.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 85°F flowing at a rate of 15 lb_m/min, and the other is pure water at 70°F flowing at 10 lb_m/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 C_p = 1 Btu/(lb_m ∙ °F).

(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.