A steam coil is immersed in a stirred heating tank. Saturated steam at 7.50 bars condenses within the coil, and the condensate emerges at its saturation temperature. A solvent with a heat capacity of 2.30 kJ/kg·°C 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. 

a. Write a differential energy balance on the tank contents. 

b. Simplify the balance to derive the steady-state outlet solvent temperature. 

c. Integrate the balance equation to calculate the time required to heat the solvent to an arbitrary temperature Tf(°C). 

d. Calculate the solvent temperature after 40 min