Question:easy

An air conditioning system mixes 30% fresh air at 35 $^\circ$C DBT and 50% RH with 70% recirculated air at 35 $^\circ$C DBT and 50% RH. Which of the following statements about "mixed air condition" is true?

Show Hint

For the adiabatic mixing of two air streams, remember that the governing conservation laws map out linearly on a psychrometric chart. As a result, the mixed state point always lies on the straight line connecting the two initial states. The distance from each initial state to the final state is inversely proportional to their respective air masses.
Updated On: Jul 4, 2026
  • The mixed air DBT will be 25 $^\circ$C
  • The mixed air humidity ratio will be equal to the arithmetic mean of two humidity ratios
  • The mixed air state point will lie on the straight line joining the two states on the psychrometric chart
  • The relative humidity of the mixed air will be equal to 50%
Show Solution

The Correct Option is C

Solution and Explanation

When two streams of moist air are mixed together with no heat added or removed, the dry air, moisture and heat content of the final mixture must all sit somewhere between the two starting streams, weighted by how much of each stream went into the mix. On a psychrometric chart this weighted averaging always places the mixed state exactly on the straight line joining the two original state points, closer to whichever stream contributed more mass, this is simply a graphical form of the mass and energy balance and holds true no matter what the two starting conditions are. Here both streams happen to sit at the very same point on the chart (35 \(^\circ\)C, 50% RH), so the mixture point does not move anywhere and lands right back on that same point, which is still a (degenerate) case of lying on the joining line. Checking the other statements: the mixed DBT works out to 35 \(^\circ\)C, not 25 \(^\circ\)C, so that option fails; the humidity ratio only equals a simple 50-50 average when the two mass flows are equal, but here the split is 30 percent to 70 percent, so that option fails too; and the mixed RH landing at 50% is just a coincidence of the two streams being identical, not a general rule. The one statement that is always true for any adiabatic mixing process is that the mixed state lies on the line joining the two original states, option (C).
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