Density Air

Overview

Engineering reference data for Density Air in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Moist Air Density Equations

The density of a moist air mixture can be calculated using specific relationships derived from the ideal gas law and the properties of its component gases.

Density from Specific Volume

Based on the specific volume of the air-vapor mixture, the density (ρ) is calculated as:

$$\rho = \frac{1}{v} = \frac{p}{R_a T} \cdot \frac{1 + x}{1 + x \left(\frac{R_w}{R_a}\right)}$$

where:

• $v$ = specific volume of moist air per mass unit of dry air and water vapor (m³/kg)
• $p$ = total pressure in the moist air (Pa)
• $R_a$ = gas constant for dry air (286.9 J/kg·K)
• $R_w$ = gas constant for water vapor (461.5 J/kg·K)
• $T$ = absolute dry bulb temperature (K)
• $x$ = humidity ratio (kg water / kg dry air)

Density Relative to Dry Air

Letting $\rho_{ref} = p / (R_a T)$ represent the density of dry air at the same total pressure, the relationship simplifies to:

$$\rho = \rho_{ref} \cdot \frac{1 + x}{1 + 1.609 x}$$

where the constant 1.609 is the ratio $R_w / R_a$.

Key Property: Dry Air is Denser than Moist Air

A critical property revealed by the density equation is that adding water vapor to air decreases the mixture's density. Since the molecular weight of water vapor (18 g/mol) is less than that of oxygen (32 g/mol) and nitrogen (28 g/mol), which dominate dry air, replacing dry air molecules with water vapor molecules results in a less dense mixture at the same temperature and pressure.

References

• Original Source