gen-define-the-water-vapor-saturation-curve-and-give-one-short-w-2ab5

Define the water vapor saturation curve and give one short worked example.

# Water Vapor Saturation Curve ## Definition The **water vapor saturation curve** is a graph showing the relationship between temperature and the maximum amount of water vapor that air can hold at saturation (100% relative humidity). It represents the **saturation vapor pressure** (es) as a function of temperature. Key points: - The curve increases exponentially with temperature (warmer air holds more moisture) - At any point on the curve, the air is saturated (RH = 100%) - Below the curve: unsaturated air - Above the curve: supersaturated (unstable, leads to condensation) The saturation vapor pressure is commonly approximated by the **Clausius-Clapeyron equation** or empirical formulas like **Magnus formula**: $$e_s = 6.11 \times 10^{7.5T/(237.3+T)} \text{ hPa}$$ where T is temperature in °C. ## Worked Example **Problem:** Air at 20°C has a vapor pressure of 15 hPa. Is it saturated? What is the relative humidity? **Solution:** 1. Find saturation vapor pressure at 20°C using Magnus formula: $$e_s = 6.11 \times 10^{7.5(20)/(237.3+20)} = 6.11 \times 10^{0.582} = 23.4 \text{ hPa}$$ 2. Compare actual vapor pressure (e = 15 hPa) to saturation: - Since 15 < 23.4 hPa, the air is **not saturated** 3. Calculate relative humidity: $$RH = \frac{e}{e_s} \times 100\% = \frac{15}{23.4} \times 100\% = 64\%$$