Question

The dry bulb temperature and relative humidity of air inside a storage chamber are 37°C and 50%, respectively. The saturation pressure of water vapour at 37°C and barometric pressure are 6.28 kPa and 101.32 kPa, respectively. The humidity ratio of air inside the chamber is _________ \text{ kg water / kg dry air}. (Round off to three decimal places.)

Hint:

The humidity ratio can be calculated by multiplying the vapor pressure by 0.622 and dividing by the dry air pressure.

Answer 1

Correct Answer: 0.017

The humidity ratio \( \omega \) is given by:
\[ \omega = 0.622 \frac{p_v}{p_a} \] Where:
- \( p_v = \phi \cdot p_{\text{sat}} \) (vapor pressure)
- \( p_a = p_{\text{atm}} - p_v \) (dry air pressure)
- \( \phi = 50% \) (relative humidity)
- \( p_{\text{sat}} = 6.28\ \text{kPa} \) (saturation pressure)
- \( p_{\text{atm}} = 101.32\ \text{kPa} \) (barometric pressure)
First, calculate the vapor pressure:
\[ p_v = 0.50 \times 6.28 = 3.14\ \text{kPa} \] Now, calculate the dry air pressure:
\[ p_a = 101.32 - 3.14 = 98.18\ \text{kPa} \] Now, calculate the humidity ratio:
\[ \omega = 0.622 \times \frac{3.14}{98.18} \] \[ \omega = 0.0193\ \text{kg/kg dry air} \] Rounded to three decimals:
\[ \omega = 0.019\ \text{kg/kg dry air} \]