Temperature Of Air Given Gas Constant Of Water Calculator

Formula Used:

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

Enthalpy of Evaporation (hfg):

J/kg·K

Partial Pressure (Pw):

Partial Pressure in Air (P∞):

Gas Constant (Rw):

J/kg·K

Density (ρ):

kg/m³

Specific Heat of Air (cp):

J/kg·K

Mean Temperature (Tf):

Lewis Number (Le):

Wet Bulb Temperature (Tw):

Air Temperature (T∞):

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1. What Is The Temperature Of Air Given Gas Constant Of Water Calculator?

This calculator determines the air temperature using the enthalpy of evaporation, partial pressures, gas constant, density, specific heat, mean temperature, Lewis number, and wet bulb temperature. It's particularly useful in thermodynamics and heat transfer calculations involving evaporation processes.

2. How Does The Calculator Work?

The calculator uses the following formula:

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

Where:

\( T_{\infty} \) — Air temperature (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)
\( R_w \) — Gas constant of water vapor (J/kg·K)
\( \rho \) — Density (kg/m³)
\( c_p \) — Specific heat of air (J/kg·K)
\( T_f \) — Mean temperature (K)
\( Le \) — Lewis number (dimensionless)
\( T_w \) — Wet bulb temperature (K)

Explanation: This formula accounts for the heat and mass transfer processes involved in evaporation, relating various thermodynamic properties to determine the air temperature.

3. Importance Of Air Temperature Calculation

Details: Accurate air temperature calculation is crucial for HVAC system design, meteorological studies, industrial drying processes, and environmental control systems where evaporation plays a significant role.

4. Using The Calculator

Tips: Enter all required values in appropriate units. Ensure all inputs are positive values. The calculator will compute the air temperature based on the provided thermodynamic properties.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the Lewis number in this calculation?
A: The Lewis number represents the ratio of thermal diffusivity to mass diffusivity, indicating the relative rates of heat and mass transfer in the evaporation process.

Q2: Why is the wet bulb temperature included in the formula?
A: The wet bulb temperature represents the lowest temperature that can be reached through evaporative cooling and serves as a reference point for the calculation.

Q3: What are typical values for the gas constant of water vapor?
A: The gas constant for water vapor is approximately 461.5 J/kg·K.

Q4: How does this calculation differ from simple temperature measurements?
A: This calculation considers the complex interplay of multiple thermodynamic properties rather than relying on direct temperature measurement alone.

Q5: In what applications is this formula particularly useful?
A: This formula is valuable in psychrometric calculations, cooling tower design, evaporative cooling systems, and any application involving simultaneous heat and mass transfer.