Psychrometric chart to determine the specific humidity

Full Answer Section

• Wet-bulb temperature (T_wb): 25°C
• Dew-point temperature (T_dp): 21°C
• Specific volume of dry air (v): 0.87 m³/kg_da

Problem 2

Given:

• Pressure (P): 1 atm
• Temperature (T): 80°F
• Relative humidity (RH): 60%

Find:

• Humidity ratio (ω)
• Specific enthalpy (h)
• Specific volume (v)
• Wet-bulb temperature (T_wb)
• Dew-point temperature (T_dp)

Solution

I. Humidity ratio (ω)

The humidity ratio can be calculated using the following equation:

ω = RH * ω_s

where:

• RH is the relative humidity
• ω_s is the saturation humidity ratio at the dry-bulb temperature

The saturation humidity ratio can be calculated using the following equation:

ω_s = 6.62 * 10^(-3) * exp(17.67 * (T - 35.5) / (T + 235))

where:

• T is the dry-bulb temperature in °F

Substituting the given values into the above equations, we get:

ω = 0.6 * 0.0181 = 0.0109 kg_w/kg_da

II. Specific enthalpy (h)

The specific enthalpy can be calculated using the following equation:

h = c_p * T + ω * h_fg

where:

• c_p is the specific heat of dry air (1.005 kJ/kg_da-°C)
• h_fg is the latent heat of vaporization (2501 kJ/kg_w)

Substituting the given values into the above equation, we get:

h = 1.005 * 80 + 0.0109 * 2501 = 33.3 kJ/kg_da

III. Specific volume (v)

The specific volume can be calculated using the following equation:

v = R * T / P * (1 + ω)

where:

• R is the ideal gas constant (0.287 kJ/kg-K)

Substituting the given values into the above equation, we get:

v = 0.287 * 80 / 101.325 * (1 + 0.0109) = 0.92 m³/kg_da

IV. Wet-bulb temperature (T_wb)

The wet-bulb temperature can be calculated using the following equation:

T_wb = T - (h_w - h) / (c_p + ω * c_pw)

where:

• h_w is the enthalpy of saturated water vapor at the wet-bulb temperature
• c_pw is the specific heat of water vapor (1.84 kJ/kg_w-°C)

The enthalpy of saturated water vapor can be calculated using the following equation:

h_w = 679 * T - 22.45 * T^2 / 1000

where:

• T is the temperature in °C

Substituting the given values into the above equations, we get:

h_w = 679 * 25 - 22.45 * 25^2 / 1000 = 2363 kJ/kg_w

Now, substituting all the known

Sample Solution

Solution

To determine the specific humidity, enthalpy, wet-bulb temperature, dew-point temperature, and specific volume of the dry air using the psychrometric chart, we first need to locate the state point of the air on the chart. The state point is located at the intersection of the dry-bulb temperature line (38°C) and the relative humidity line (40%).

Once we have located the state point, we can read the following information from the chart:

• Specific humidity (ω): 0.015 kg_w/kg_da
• Enthalpy (h): 50 kJ/kg_da