Question

A steam coil is immersed in a stirred heating tank. Saturated steam at 7.50 bar condenses within the coil , and the condensate emerges at at its saturation temperature. A solvent with a heat capacity of 2.30 kJ is fed to the tank at a steady rate of 12.0 kg/min and a temperature of 25°C, and the heated solvent is discharged at the same flow rate. The tank is initially filled with 760 kg of solvent at 25°C, at which point the flows of both steam and solvent are commenced. The rate at which heat is transferred from the steam coil to the solvent is given by the expression where UA (the product of a heat transfer coefficient and the area through which the heat is transferred) equals 11.5 kJ/min·°C. The tank is well stirred, so that the temperature of the contents is spatially uniform and equals the outlet temperature.

Write a differential energy balance on the tank contents.

Answer 1

d/dt[mCp(Ts-Ti)] = FCp(Ts-Ti) - FoCp(Ts-Ti) + uA(Ts-Ti)

Step-by-step explanation:

Differential balance equation on the tank is given as;

Accumulation = energy of inlet steam - energy of outlet steam+

heat transfer from the steam

where;

Accumulation = d/dt[mcp(Ts-Ti)]

Energy of inlet steam = FCp(Ts-Ti)

Energy of outlet steam = FoCp(Ts-Ti)

Heat transfer from the steam = uA(Ts-Ti)

Substituting into the formula, we have;

Accumulation = energy of inlet steam - energy of outlet steam+

heat transfer from the steam

d/dt[mCp(Ts-Ti)] = FCp(Ts-Ti) - FoCp(Ts-Ti) + uA(Ts-Ti)