#### Degrees of Freedom: Interactive Simulation

This simulation was prepared using Mathematica. Download the free Wolfram player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. A screencast below explains how to use this simulation.

In this Demonstration, a degree-of-freedom analysis is performed on a distillation process to determine whether the system has sufficient information to solve for the unknown variables. Use buttons to select the unit on which to do mass balances (distillation column, condenser, or reboiler) or to do a balance on the overall system. When “condenser” is selected, use buttons to select “partial condenser” or “total condenser”. Set the “total number of unknowns” with the slider; unknown variables are colored blue on the diagram and known variables are black. The known variables are selected randomly, and they change when you click the “new problem” button. Use buttons to select how species B is represented: as z_{B} or as 1 – z_{A}; the degree-of-freedom analysis is different for each representation. An explanation of the analysis is shown on the right. For zero degrees of freedom, the balances are solvable. The system is overspecified if it has more equations than unknowns and it is underspecified if it has more unknowns than equations. For a reboiler, the equilibrium ratio K_{r}, is known, and for a partial condenser the equilibrium ratio K_{c} is known. Temperatures and pressures are known for this analysis. Mass balances and phase equilibrium relations are solved to determine the unknown variables.

**Try to answer these questions before determining the answer with the simulation**. We suggest that you write down the reasons for your answers.

- If you increase the number of unknowns within the same problem, does the system move toward over- or underspecification?
- How are the number of degrees affected by the switch from using 1 – z
_{A}to z_{B}as the species B representation? Explain.