Gas Constant Of Water Vapor Calculator

Formula Used:

\[ R_w = \frac{h_{fg} \times (P_w - P_{\infty})}{(T_{\infty} - T_w) \times \rho \times c_p \times T_f \times (Le^{0.67})} \]

Enthalpy of Evaporation (h_fg):

J/kg·K

Partial Pressure (P_w):

Partial Pressure in Air (P_∞):

Air Temperature (T_∞):

°C

Wet Bulb Temperature (T_w):

°C

Density (ρ):

kg/m³

Specific Heat of Air (c_p):

J/kg·K

Mean Temperature (T_f):

°C

Lewis Number (Le):

Gas Constant of Water Vapor (R_w):

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1. What is Gas Constant of Water Vapor?

The gas constant of water vapor is a fundamental thermodynamic property that relates the pressure, volume, and temperature of water vapor in the ideal gas equation. It is specific to water vapor and differs from the universal gas constant.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ R_w = \frac{h_{fg} \times (P_w - P_{\infty})}{(T_{\infty} - T_w) \times \rho \times c_p \times T_f \times (Le^{0.67})} \]

Where:

\( R_w \) — Gas constant of water vapor (J/kg·K)
\( h_{fg} \) — Enthalpy of evaporation (J/kg·K)
\( P_w \) — Partial pressure of water vapor at wet bulb temperature (Pa)
\( P_{\infty} \) — Partial pressure of water vapor in air (Pa)
\( T_{\infty} \) — Air temperature (°C)
\( T_w \) — Wet bulb temperature (°C)
\( \rho \) — Density (kg/m³)
\( c_p \) — Specific heat of air (J/kg·K)
\( T_f \) — Mean temperature (°C)
\( Le \) — Lewis number (dimensionless)

Explanation: This formula calculates the gas constant of water vapor based on thermodynamic properties and heat/mass transfer principles.

3. Importance of Gas Constant Calculation

Details: Accurate calculation of the gas constant for water vapor is crucial for various engineering applications including HVAC system design, atmospheric studies, psychrometric calculations, and heat transfer analysis involving humid air.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Ensure temperature differences are valid (T_∞ ≠ T_w), densities and specific heats are positive, and Lewis number is greater than zero for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value range for water vapor gas constant?
A: The gas constant for water vapor is approximately 461.5 J/kg·K, which is higher than the universal gas constant (287 J/kg·K for dry air).

Q2: Why is the Lewis number important in this calculation?
A: The Lewis number represents the ratio of thermal diffusivity to mass diffusivity and accounts for the coupling between heat and mass transfer processes.

Q3: How does this relate to psychrometric calculations?
A: The gas constant of water vapor is fundamental to psychrometric relationships and the calculation of various humidity parameters in air-water vapor mixtures.

Q4: What are common applications of this calculation?
A: This calculation is used in HVAC design, meteorological studies, industrial drying processes, and environmental control systems.

Q5: How accurate is this formula compared to experimental data?
A: The formula provides good accuracy for most engineering applications, though for precise scientific work, more complex equations of state may be required.