## Psychrometry Gas Vapor Mixtures

The gas - vapor mixture of greatest practical importance is the air - water system1. The thermodynamic behavior of this mixture affects the weather and engineered devices such as air conditioners. In these applications, air can be treated as an inert ideal gas.

Water vapor can be considered to behave ideally because its concentration in air is low. In this two-component gas mixture, air is treated as a single species. The gas and the vapor obey Dalton's rule (Sect. 7.2):

where the subscripts w and a denote water vapor and air (or other inert gas). pw and pa are the partial pressures of water vapor and air, respectively, and p = pw + pa is the total pressure, which is fixed by pa. Psychrometry problems frequently deal with water vapor

1 Reference 1 (p. 252) gives a short discussion of gas-vapor mixtures.

in equilibrium with liquid water. In the two-phase case, the gas phase is said to be saturated, and pw = psat,w is a property of water; if no liquid water is present, pw is an adjustable parameter like pa. The relative humidity ^ quantitatively characterizes the water content of air as the ratio of the partial pressure of water to its vapor pressure:

Because the temperature in practical applications is generally between 0 and 100oC, the representation of psat,w by the Clausius-Clapyron equation is simpler and sufficiently accurate. In this temperature range, the vapor pressure of water is adequately represented by Eqs (5.9) and (5.10):

Like all thermodynamic properties of a pure substance, the vapor pressure is in principle a function of two variables. Eq (5.13) shows only the temperature dependence. There is a also dependence of psat,w on total pressure, but this effect is very small (see problem 5.15)

Equation (5.13) gives the partial pressure of water vapor in saturated air at a specified temperature. The inverse representation of saturation gives the temperature at which saturation occurs in air with a specified water vapor partial pressure. This temperature is called the dew point because the phenomenon describes the first appearance of dew on grass as the night air cools. The dew point is obtained from Eq (5.13) by replacing psat,w by pw and T by TDP, the dew point:

The onset of liquid water condensation is illustrated in the p-T diagram of Fig. 5.3. The unsaturated air in state 1 has a relative humidity given by pw/psat,w(T1), where pw is specified. psat,w(T1) is located at point 1' on the liquid-vapor co-existence curve. When this gas is cooled at constant total pressure, both pw and pa remain constant until the saturation curve at state 2 is reached. The temperature at state 2 is the dew point given by Eq (5.14). Upon further cooling from state 2 to state 3, water condenses from the gas, pw (now equal to psat,w) decreases as determined by Eq (5.13), and pa increases to keep the total pressure constant. The following example illustrates this process in detail.

Fig. 5.3 The p - T diagram of water showing one unsaturated state (No. 1) and two saturated states ( Nos. 2 and 3)

temperature, K

Fig. 5.3 The p - T diagram of water showing one unsaturated state (No. 1) and two saturated states ( Nos. 2 and 3)

Example: Unsaturated air is cooled from state 1 to state 3 in a piston/cylinder container maintained at a constant pressure of 1 atm.

Calculate the:

(a) dew point of the gas in state 1

(b) fraction of water condensed at state 3

(c) heat removed from the container per mole of air during cooling from state 1 to state 2 and from state 2 to state 3.

(a) The saturation pressure associated with the air temperature of state 1 is on the liquid-vapor curve in Fig. 5.3 (point 1') directly above point 1. As calculated from Eq (5.13) for Ti = 35.2oC (308.2 K), psat1 = 0.0568 atm. The relative humidity is 70%, so Eq (5.12) gives pw1 = 0.0398 atm. Because the air is just saturated in state 2, the water partial pressure does not change on cooling from 1 to 2 and psat2 = pw2 = pw1. The dew point of air with this partial pressure of water lies on the saturation curve at state 2 in Fig. 5.3. From Eq (5.14), T2 = Tdp = 301.9 K (28.9oC).

(b) The fraction of the water vapor in the gas phase in state 1 (or in state 2) that condenses when state 3 is attained is determined by combining Dalton's rule and the vapor pressure curve. The number of moles of water (nw) per mole of air (na) in the gas in states 1 and 2 is determined from Eq (5.11):

## Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

Get My Free Ebook

### Responses

• lily
What is gas mixture in thermodynamics?
8 years ago