Question

During a steady state air-conditioning process, air enters a heating section at 15°C with 40% relative humidity and leaves at 30°C. Assuming the heating process takes place at 100 kPa, the relative humidity of the air at exit is _________ % (round off to nearest integer). Saturation pressures of water vapor at 15°C and 30°C are 1.7057 kPa and 4.2469 kPa respectively.

Hint:

Relative humidity changes based on the saturation pressure at the given temperature. The mass of water vapor remains constant during the process.

Answer 1

Correct Answer: 15

At the inlet: \[ P_{sat,15°C} = 1.7057\ \text{kPa}, \quad P_{sat,30°C} = 4.2469\ \text{kPa} \] Relative humidity at the inlet: \[ RH_1 = 40% = 0.40 \] The partial pressure of water vapor at the inlet: \[ P_v = RH_1 \times P_{sat,15°C} = 0.40 \times 1.7057 = 0.68228\ \text{kPa} \] Now, at the exit (30°C): The specific volume of the air and amount of water vapor are unchanged during the process. So, the partial pressure of water vapor at the exit: \[ P_v = P_{v,exit} = \text{same} = 0.68228\ \text{kPa} \] The relative humidity at 30°C: \[ RH_2 = \frac{P_v}{P_{sat,30°C}} = \frac{0.68228}{4.2469} = 0.1604 \] Thus, the relative humidity at the exit is: \[ RH_2 = 16% \] \[ \boxed{16%} \]