How Do You Calculate Saturated Vapor Pressure

Magnus Formula:

\[ e_s = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right) \]

Saturated Vapor Pressure (e_s):

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1. What is Saturated Vapor Pressure?

Saturated vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature. It represents the maximum amount of water vapor the air can hold at a specific temperature.

2. How Does the Magnus Formula Work?

The calculator uses the Magnus formula:

\[ e_s = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right) \]

Where:

\( e_s \) — Saturated vapor pressure (hPa)
\( T \) — Temperature (°C)
\( \exp \) — Exponential function

Explanation: The Magnus formula is an empirical relationship that approximates the relationship between temperature and the saturation vapor pressure of water. The constants 6.112, 17.67, and 243.5 are empirically derived values that make the formula accurate for meteorological applications.

3. Importance of Saturated Vapor Pressure Calculation

Details: Calculating saturated vapor pressure is essential in meteorology, HVAC design, agricultural planning, and various industrial processes. It helps determine humidity levels, predict fog formation, and understand evaporation rates.

4. Using the Calculator

Tips: Enter temperature in degrees Celsius. The formula is valid for temperatures between -50°C and 60°C, which covers most environmental conditions.

5. Frequently Asked Questions (FAQ)

Q1: Why is the Magnus formula used instead of other equations?
A: The Magnus formula provides a good balance between accuracy and computational simplicity, making it widely used in meteorological applications.

Q2: What are typical values of saturated vapor pressure?
A: At 0°C, e_s is approximately 6.11 hPa; at 20°C, it's about 23.39 hPa; and at 40°C, it reaches around 73.78 hPa.

Q3: How does saturated vapor pressure relate to relative humidity?
A: Relative humidity is the ratio of actual vapor pressure to saturated vapor pressure, expressed as a percentage.

Q4: Does the formula work for all temperatures?
A: The Magnus formula is most accurate between -45°C and 60°C. For extreme temperatures, more complex equations like the Goff-Gratch formula may be used.

Q5: Why are there different constants in various versions of the Magnus formula?
A: Different researchers have derived slightly different constants based on their experimental data and the temperature ranges they focused on.