How do you calculate mixed-air enthalpy from outdoor and return air enthalpies and outdoor-air fraction?

How do you calculate mixed-air enthalpy from outdoor and return air enthalpies and outdoor-air fraction?

• A. h_mix = h_outdoor + h_return
• B. h_mix = h_outdoor - h_return
• C. h_mix = f_outdoor * h_outdoor + (1 - f_outdoor) * h_return
• D. h_mix = f_outdoor * h_return + (1 - f_outdoor) * h_outdoor

Answer: (C)

When outdoor air and return air mix, the resulting enthalpy is a weighted average based on how much of each stream is present. The outdoor-air fraction represents the portion of the mixed air that comes from outdoors, while the remainder comes from return air. So the enthalpy of the mix is h_mix = f_outdoor × h_outdoor + (1 − f_outdoor) × h_return. This reflects the energy each stream contributes per unit mass to the mixed air. For example, with h_outdoor = 500 kJ/kg, h_return = 400 kJ/kg, and f_outdoor = 0.2, the mix enthalpy is 0.2×500 + 0.8×400 = 420 kJ/kg. The other forms would either ignore the weighting or swap the contributions, which doesn’t match how mixing distributes energy.

When outdoor air and return air mix, the resulting enthalpy is a weighted average based on how much of each stream is present. The outdoor-air fraction represents the portion of the mixed air that comes from outdoors, while the remainder comes from return air. So the enthalpy of the mix is h_mix = f_outdoor × h_outdoor + (1 − f_outdoor) × h_return. This reflects the energy each stream contributes per unit mass to the mixed air. For example, with h_outdoor = 500 kJ/kg, h_return = 400 kJ/kg, and f_outdoor = 0.2, the mix enthalpy is 0.2×500 + 0.8×400 = 420 kJ/kg. The other forms would either ignore the weighting or swap the contributions, which doesn’t match how mixing distributes energy.