Question

Psychrometric ratio for air-water mixture over the temperature usually come across is approximately______

• A. 1
• B. 0.5
• C. \( \infty \)
• D. 0

Hint:

For any gas-vapor mixture other than air-water (e.g., benzene-air or ethanol-air), the psychrometric ratio is significantly different from 1.
In those cases, the wet-bulb temperature is distinct from the adiabatic saturation temperature.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the approximate value of the psychrometric ratio for an air-water vapor mixture under typical ambient temperature conditions.
This is a standard property value in humidification and psychrometrics.

Step 2: Key Formula or Approach:
The psychrometric ratio is defined as the ratio of the heat transfer coefficient (\( h_G \)) to the product of the mass transfer coefficient (\( k_Y \)) and the humid heat (\( C_s \)):
\[ r = \frac{h_G}{k_Y \cdot C_s} \]
This ratio is also related to the Lewis number (\( Le \)) by:
\[ r \approx Le^{2/3} = \left(\frac{Sc}{Pr}\right)^{2/3} \]

Step 3: Detailed Explanation:

• The Lewis Relation: For many gas-vapor mixtures, the rates of heat and mass transfer are different.
However, for an air-water vapor mixture at normal temperatures, the thermal diffusivity and molecular diffusivity are nearly equal.
This results in a Lewis number close to unity:
\[ Le = \frac{Sc}{Pr} \approx 1.0 \]

• Psychrometric Ratio Value: Since the Lewis number is approximately 1, the psychrometric ratio for the air-water system is also very close to 1:
\[ r \approx 1.0 \]

• Practical Consequence: Because the psychrometric ratio is close to 1 for the air-water system, the wet-bulb temperature (\( T_w \)) is approximately equal to the adiabatic saturation temperature (\( T_{as} \)).
This simplification is unique to the air-water system and does not apply to other organic solvent-air systems.


Step 4: Final Answer:
The psychrometric ratio for an air-water mixture is approximately 1.