Degrees of freedom, steady and unsteady balances, recycle and purge, reactive systems, humidity and combustion.
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- What is degrees of freedom in process calculations?
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The number of independent variables that must be specified to completely define the state of a system.
- Write the degrees of freedom equation.
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DOF = N - E, where N is the number of variables and E is the number of independent equations.
- What does DOF = 0 mean for a process?
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The system is completely specified and can be solved with the available information.
- What does DOF > 0 indicate?
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The system is under-specified; additional information or constraints are needed.
- List typical types of equations counted in DOF analysis.
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Material balances, energy balances, equilibrium relations, physical property relations, and stoichiometric equations.
- In steady-state operation, which term in the general balance equation equals zero?
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The accumulation term (dM/dt or dE/dt) equals zero because system properties do not change with time.
- Write the steady-state material balance equation for a flow process.
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Input mass rate = Output mass rate, or sum of mass in = sum of mass out.
- Write the steady-state energy balance equation for a flow process.
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Energy in + work in = Energy out + work out, or in rate form: rate in + rate of work in = rate out + rate of work out.
- When can steady-state assumptions be applied?
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When operating conditions do not change with time and the system has reached equilibrium after startup.
- What is unsteady-state operation?
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Operation where system properties or conditions change with time, so the accumulation term in the balance is not zero.
- Give three examples of unsteady-state processes.
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Filling or draining a tank, batch reactions, and system startup or shutdown.
- In unsteady-state balances, what term represents accumulation?
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The accumulation term dM/dt or dE/dt, representing the rate of change of mass or energy in the system with respect to time.
- What initial condition is required to solve unsteady-state balance differential equations?
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The initial amount, concentration, or temperature of the material or energy in the system at time t = 0.
- What is a recycle stream in a process?
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A portion of the outlet stream that is returned to the inlet and mixed with fresh feed.
- Name three reasons to use recycle in a process.
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To improve conversion of reactants, recover valuable unreacted material, or increase selectivity to desired products.