莫里爾圖（i-x 圖）／焓濕圖：濕空氣範例

概述

The Mollier diagram (also called the Mollier i-x chart) is a graphical representation of the thermodynamic properties of moist air. It plots enthalpy against specific humidity (moisture content), with overlay lines for dry bulb temperature, wet bulb temperature, and relative humidity. The Mollier diagram is a rotated variant of the standard psychrometric chart and is widely used in HVAC system design for analyzing heating, cooling, humidification, dehumidification, and air mixing processes.

關键公式

Humidity Ratio (Specific Humidity)

$\omega = 0.622 \frac{P_v}{P_a}$

The mass of water vapor per unit mass of dry air, where $P_v$ is the partial pressure of water vapor and $P_a$ is the partial pressure of dry air.

Relative Humidity

$\phi = \frac{P_v}{P_{vs}} \times 100\%$

The ratio of actual vapor pressure to saturation vapor pressure at the same dry bulb temperature.

Enthalpy of Moist Air

$h = c_p \cdot T_{db} + \omega \cdot h_g$

Sensible heat plus latent heat per unit mass of dry air. The constant $c_p \approx 1.006$ kJ/(kg·°C) for dry air and $h_g$ is the enthalpy of saturated water vapor at the given temperature.

Wet Bulb Temperature

$T_{wb} \approx T_{db} - \frac{P_{vs} - P_v}{\gamma}$

此近似式將濕球溫差與水蒸氣壓差聯繫起來，其中 $\gamma$ 為乾濕球常數（在 1 atm 下約為 66.6 Pa/°C）。

變量

Example: Reading the Mollier Diagram

Case 1 — Known: Dry Bulb Temperature and Relative Humidity

Given Tdb = 21 °C and φ = 50%, read the following from the Mollier chart:

Case 2 — Known: Dry Bulb and Wet Bulb Temperatures

Given Tdb = 19 °C and Twb = 12 °C, read:

Saturation Vapor Pressure Reference

The saturation vapor pressure $P_{vs}$ increases sharply with temperature. Representative values from the Antoine equation or steam tables:

Mollier Chart Example Points

The original images show example readings from the Mollier chart. The extracted readings are represented below as data so they can be inspected without relying only on the bitmap chart.

Mollier Diagram Reproduction

The original Mollier diagram is redrawn below as an equation-generated psychrometric chart for moist air at standard atmospheric pressure. The chart uses humidity ratio on the horizontal axis and dry-bulb temperature on the vertical axis, with relative-humidity curves, constant-enthalpy lines, humidity-ratio grid lines, and the saturation boundary.

Mollier vs. Psychrometric Chart

The Mollier diagram and the standard ASHRAE psychrometric chart display the same thermodynamic data but with different axis orientations:

Calculator: Humidity Ratio from Vapor Pressure

單位換算器

Note: the direct kJ/kg to Btu/lb conversion preserves the metric enthalpy reference. The IP psychrometric enthalpy value uses the common inch-pound psychrometric reference and should be used when comparing with IP psychrometric charts.

Mollier Chart Reading Examples

The annotated example charts below are redrawn from the same psychrometric equations used by the main chart.

工程要點

• Atmospheric pressure matters. The Mollier diagram is typically drawn for standard atmospheric pressure (101.325 kPa). At significantly different altitudes or pressures, corrections are needed or a pressure-specific chart should be used.
• Axis orientation can confuse users. In the Mollier chart enthalpy runs nearly vertically and humidity ratio nearly horizontally, which is the reverse of what many ASHRAE-trained engineers expect. Verify which axis convention your chart uses before reading values.
• Chart accuracy. Reading values from a printed chart introduces interpolation error. For precise calculations use the governing equations or digital psychrometric tools rather than visual interpolation.
• Wet bulb temperature approximations. The formula $T_{wb} \approx T_{db} - \frac{P_{vs} - P_v}{\gamma}$ is a linearization. For high accuracy, use iterative thermodynamic models (e.g., ASHRAE's formulation) or ASHRAE Psychrometric Chart No. 1.
• Process visualization. The Mollier diagram excels at visualizing air-handling processes: sensible heating moves horizontally to the right; cooling and dehumidification move down and left; mixing of two airstreams follows a straight line between their state points.
• Saturation line. The curved boundary on the Mollier chart represents 100% relative humidity. Air states cannot exist above (to the right of) this line—condensation occurs beyond saturation.

參考资料

• Original Source — Engineering ToolBox: Psychrometric Chart / Mollier Diagram
• ASHRAE Handbook — Fundamentals, Psychrometrics chapter