2.1 Intensive and Extensive Variables

Chemical processes involve two key types of variables: intensive and extensive. Intensive variables, like temperature and pressure, stay constant regardless of system size. Extensive variables, such as mass and volume, change proportionally with the system's size.

Understanding these variables is crucial for chemical engineers. Intensive variables help determine a system's state, while extensive variables are used in overall balances. This knowledge is essential for accurate process analysis, scaling, and design in chemical engineering.

Understanding Intensive and Extensive Variables in Chemical Processes

Intensive vs extensive variables

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• Intensive variables remain constant regardless of system size measured at a single point (temperature, pressure, density)
• Extensive variables scale proportionally with system size measured for entire system (mass, volume, energy)

Independence from system size

• Intensive variables unchanged when system divided or combined (viscosity, specific heat capacity)
• Extensive variables change when system divided or combined can be converted to intensive by dividing by mass or moles

Relationships in chemical properties

• Density (intensive): $\rho = \frac{m}{V}$ where mass and volume are extensive
• Specific heat (intensive): $c_p = \frac{C_p}{m}$ where heat capacity and mass are extensive
• Concentration (intensive): $c = \frac{n}{V}$ where moles and volume are extensive

Applications in process analysis

• Mass balance calculations use extensive variables for overall balances (mass, moles) and intensive for component balances (concentration)
• Energy balance calculations use extensive variables for system-wide balances (total energy, enthalpy) and intensive for state determinations (temperature, pressure)
• Scaling processes: extensive variables scale proportionally while intensive remain constant
• Mixing problems use extensive variables to calculate total quantities and intensive to determine final mixture properties
• Phase equilibrium calculations use intensive variables to determine equilibrium states (temperature, pressure, composition)
• Reactor design uses extensive variables for overall material and energy balances and intensive for reaction rate and equilibrium calculations