2. Air in a room is at 75°F dry bulb and 60% relative humidity. Calculate the following
properties of the air:
a) partial pressure of water vapor in the air, in psia
b) humidity ratio, in lbm water/ibm dry air
c) enthalpy, in Btu/lbm dry air
d) dew-point temperature, in °F
Answers
To calculate these properties, we need to use psychrometric charts or equations. Here are the calculations:
a) The partial pressure of water vapour in the air can be found using the following equation:
pw = phi * pg
where pw is the partial pressure of water vapour, phi is the relative humidity (expressed as a fraction), and pg is the saturation pressure of water vapour at the air temperature (from the psychrometric chart or equation). For 75°F, pg is approximately 0.53 psia. So, we have:
pw = 0.6 * 0.53 = 0.318 psia
b) The humidity ratio is the ratio of the mass of water vapour to the mass of dry air in the mixture. It can be calculated using the following equation:
W = 0.62198 * pw / (p - pw)
where W is the humidity ratio, pw is the partial pressure of water vapour (from part a), p is the total pressure of the air (assumed to be atmospheric pressure, which is approximately 14.7 psia), and 0.62198 is the ratio of the molecular weight of water vapour to that of dry air. Substituting the values, we get:
W = 0.62198 * 0.318 / (14.7 - 0.318) = 0.0106 lbm water/ibm dry air
c) The enthalpy of the air can be found using the following equation:
h = 1.007 * t + W * (1061 + 0.444 * t)
where h is the enthalpy, t is the dry bulb temperature in °C (converted from 75°F), and W is the humidity ratio (from part b). Substituting the values, we get:
h = 1.007 * (75 - 32) / 1.8 + 0.0106 * (1061 + 0.444 * (75 - 32) / 1.8) = 32.24 Btu/lbm dry air
d) The dew point temperature is the temperature at which the air would be saturated and water vapour would start to condense out as liquid water. It can be found using the psychrometric chart or equation. From the chart, the dew point temperature for 0.318 psia partial pressure of water vapour is approximately 56°F.