Psychrometrics: 3 Worked Examples

Updated October 2026

These three problems cover the three ways this calculator's "second known value" dropdown can be used — RH, dew point, and wet-bulb — each worked fully by hand using the exact formulas behind the tool, so you can check your own work or follow the method step by step.

Example 1 — Given dry-bulb and RH, find everything else

Given: Tdb = 25°C, RH = 50%, P = 101.325 kPa.

  1. Saturation pressure: es(25) = 0.61078 × exp(17.27×25/262.3) ≈ 3.17 kPa.
  2. Vapor pressure: e = 0.50 × 3.17 = 1.58 kPa.
  3. Humidity ratio: W = 0.622 × 1.58 / (101.325−1.58) ≈ 0.00988 kg/kg (9.88 g/kg).
  4. Dew point (invert Tetens): ln(1.58/0.61078) = 0.950; Tdp = 237.3×0.950/(17.27−0.950) ≈ 13.9°C.
  5. Wet-bulb (solve psychrometer equation by bisection): Twb ≈ 18.0°C.
  6. Enthalpy: h = 1.006×25 + 0.00988×(2501+1.86×25) ≈ 50.3 kJ/kg.
  7. Specific volume: v = 0.287×298.15×(1+1.6078×0.00988)/101.325 ≈ 0.858 m³/kg.

Example 2 — Given dry-bulb and dew point, find RH, humidity ratio and enthalpy

Given: Tdb = 30°C, Tdp = 15°C, P = 101.325 kPa.

  1. es(30) ≈ 4.24 kPa (saturation at dry-bulb).
  2. e = es(15) ≈ 1.71 kPa (dew point's own saturation value is the actual vapor pressure, by definition).
  3. RH: e/es(Tdb) = 1.71/4.24 ≈ 40.2%.
  4. Humidity ratio: W = 0.622×1.71/(101.325−1.71) ≈ 0.01065 kg/kg (10.65 g/kg).
  5. Enthalpy: h = 1.006×30 + 0.01065×(2501+1.86×30) ≈ 57.4 kJ/kg.

Example 3 — Given dry-bulb and wet-bulb, find RH

Given: Tdb = 35°C, Twb = 24°C, P = 101.325 kPa.

  1. Apply the psychrometer equation directly (Twb is already known, so no bisection needed): e = es(24) − 0.000662×P×(Tdb−Twb).
  2. es(24) ≈ 2.98 kPa; correction term 0.000662×101.325×11 ≈ 0.74 kPa.
  3. e = 2.98 − 0.74 = 2.25 kPa.
  4. es(35) ≈ 5.63 kPa.
  5. RH: 2.25/5.63 ≈ 40.0%.

Notice this is the reverse direction from the normal bisection case — when wet-bulb is already known, the psychrometer equation can be solved directly for e with no iteration required, because Twb is no longer the unknown.

Checking your own work against the calculator

Enter each example's given values into the calculator directly and confirm the outputs match — this is the fastest way to validate hand calculations for an exam or a homework set, and to build intuition for which direction each formula needs to be solved.

FAQ

Why does Example 3 not need bisection, while the homepage calculator does?
Because when wet-bulb is already the known input, the psychrometer equation only has one unknown (e), which can be isolated directly. Bisection is only needed when wet-bulb itself is the unknown being solved for, as in Example 1.
Can I use these same steps for a Fahrenheit/imperial problem?
Convert to °C and kPa first (the calculator does this automatically when you select °F), run the same formulas, then convert results back if needed — the underlying equations are defined in °C and kPa.
Where can I check a wet-bulb bisection result like Example 1's by hand?
Pick a candidate Twb, plug it into the psychrometer equation, and see whether the result is above or below your target e — then narrow your guess and repeat. See the wet-bulb page for the full method.

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