Question

Unit of Mixing Ratio is

• A. %
• B. kg/$m^3$
• C. kg/kg
• D. $m^3/m^3$

Hint:

Mixing ratio is the ratio of mass of water vapor to the mass of dry air. Because both are mass units, the ratio is expressed as mass/mass, which is kg/kg.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In meteorology and atmospheric physics, the mixing ratio ($r$) is an absolute measure of humidity.
It represents the mass of water vapor present in a given volume of air relative to the mass of dry air in that same volume.

Step 2: Key Formula or Approach:
The mixing ratio is mathematically expressed as:
\[ r = \frac{m_v}{m_d} \]
where $m_v$ is the mass of water vapor, and $m_d$ is the mass of dry air.

Step 3: Detailed Explanation:
Let us analyze the units of the variables in the formula:
- The mass of water vapor ($m_v$) is measured in kilograms ($\text{kg}$).
- The mass of dry air ($m_d$) is also measured in kilograms ($\text{kg}$).
- Therefore, the mixing ratio is a dimensionless ratio of mass to mass, standardly expressed in the unit kg/kg (or grams per kilogram, g/kg, for practical meteorological scales).
Let us review the incorrect options:
- Option (A) %: Unit for Relative Humidity.
- Option (B) kg/$\text{m^3$:} Unit for Absolute Humidity (mass of water vapor per unit volume of air).
- Option (D) $\text{m^3/\text{m}^3$:} Unit for volumetric soil water content, not atmospheric mixing ratio.
Thus, the correct unit is kg/kg.

Step 4: Final Answer:
The unit of mixing ratio is kg/kg.