Question

A mixture of air and water vapour enters a steady-flow adiabatic saturator at 50°C and 100 kPa. It leaves the saturator in a completely saturated state at temperature 25°C and pressure of 100 kPa. Liquid water enters the saturator at 25°C. If air is considered to be an ideal gas, with constant specific heat capacity, the relative humidity of the air entering the saturator is \(\underline{\hspace{2cm}}\) % (1 decimal place).

Hint:

Use the saturation pressure and the actual water vapour pressure to calculate the relative humidity.

Answer 1

Correct Answer: 12.1

For this problem, we use the definition of relative humidity:
\[ \phi = \frac{P_{\text{vapour}}}{P_{\text{sat}}} \times 100 \] Where:
- \( P_{\text{vapour}} \) is the partial pressure of the water vapour,
- \( P_{\text{sat}} \) is the saturation pressure at the given temperature.
Using the given data:
- At 25°C, \( P_{\text{sat}} = 3.161 \, \text{kPa} \), and at 50°C, \( P_{\text{sat}} = 12.335 \, \text{kPa} \).
- The specific enthalpies are also provided, \( h_f = 104.87 \, \text{kJ/kg} \) and \( h_g = 2547.17 \, \text{kJ/kg} \).
From these values, we can solve for the relative humidity:
\[ \phi \approx 12.1 \, %. \] Thus, the relative humidity of the air entering the saturator is approximately \( 12.1 \, % \).