Question

A room contains air at 25°C, 100 kPa and 80% relative humidity. Saturation pressure of water vapor at 25°C is 3.1698 kPa. Find the specific humidity (kg water vapor/kg dry air). Round off to 4 decimals.

Hint:

Relative humidity gives actual vapor pressure. Use \( \omega = 0.622 \frac{p_v}{P - p_v} \) for specific humidity.

Answer 1

Correct Answer: 0.016

Actual vapor pressure:
\[ p_v = \phi\, p_{sat} = 0.8 \times 3.1698 = 2.53584\ \text{kPa} \] Specific humidity formula:
\[ \omega = 0.622 \frac{p_v}{P - p_v} \] Substitute:
\[ \omega = 0.622 \frac{2.53584}{100 - 2.53584} \] \[ \omega = 0.622 \frac{2.53584}{97.46416} \] \[ \omega = 0.01616 \] Rounded to 4 decimals:
\[ \omega = 0.0162 \]