Question

The virtual temperature correction for moist air at 40$^\circ$C that has a mixing ratio of 25 g kg$^{-1}$ is :

• A. 4.8 K
• B. 5.8 K
• C. 6.8 K
• D. 7.8 K

Hint:

Moist air is lighter than dry air. Therefore, the "virtual" temperature of moist air is always higher than its actual temperature.

Answer 1

The Correct Option is A

Concept: Virtual temperature ($T_v$) is the temperature at which dry air would have the same density as moist air at the same pressure. The correction ($\Delta T = T_v - T$) accounts for the fact that water vapor is less dense than dry air.

Step 1: Identify the Formula.
The approximation for virtual temperature is: \[ T_v \approx T(1 + 0.61w) \] Where $T$ is the absolute temperature in Kelvin and $w$ is the mixing ratio in kg/kg.

Step 2: Convert Units.

• Temperature $T = 40^\circ\text{C} + 273.15 = 313.15$ K
• Mixing ratio $w = 25 \text{ g/kg} = 0.025 \text{ kg/kg}$

Step 3: Calculate the Correction.
The correction is $\Delta T = T_v - T = T(0.61w)$: \[ \Delta T = 313.15 \times 0.61 \times 0.025 \] \[ \Delta T \approx 313.15 \times 0.01525 \approx 4.775 \text{ K} \] Rounding gives approximately 4.8 K.