S5. A large mixing tank contains a moderate amount of hot water, m0. A cold water spigot is suddenly turned on, adding water to the tank at a rate of min and of a temperature Tin. At the same time, an electrical heating element in the tank is turned on along with the shaft motor. a) Determine the simplified mass balance. Solve the expression for the system mass as a function of time explicitly: msys(t) b) Determine the simplified energy balance applicable during the filling process c) Beginning with your simplified energy balance, develop the differential equation for the system temperature as a function of time applicable during the filling process. d) Use U-substitution to solve the resulting differential equation. Solve the expression for the system temperature as a function of time: Tsys(t). e) Determine the symbolic expression for the steady state temperature. Hint: Do not neglect the expansion work that occurs because the system volume is increasing as the tank fills. Is the system pressure constant in this system? If so, you can take the P inside the derivative (PdV/dt) and combine with dU/dt. Recall that H=U+PV