SKMM2423Applied Thermodynamics

Psychometry and Air-conditioning

Introduction..

• Psychrometry is the study of thermodynamic properties of air and water vapormixtures (moist air)

• Air is made up of five main gases:1. Nitrogen (78.03%)2. Oxygen (20.99%)3. Argon (0.94%)4. Carbon dioxide (0.03%)5. Hydrogen (0.01%)

• Water vapor adds some complexity because it might condense.

• Applications:-Air conditioning-Cooling towers-Meteorology-Industrial processes (Drying)

Background-Gas Mixtures

• Apply the rules for determining mixture properties to ideal-gas mixtures.

• Predict the P-v-T behavior of gas mixtures based on Dalton’s law

• Understand the concept of partial pressures.

Gas Mixture - Dalton’s ModelPartial Pressures

A relationship exists between the totalpressure and individual partial pressures by using “MOLE FRACTION”

Dalton’s Law

• Mole fraction (X): a dimensionless number that expresses the ratio of the number of moles of one component compared to the total number of moles in a mixture.

What is mole fraction??

Example of Calculation of Mole Fraction

• If a gas mixture contains 5.0 mol O2 (g), 3.0 mol H2O (g), and 12.0 mol N2 (g),

XO2=

** You must be able to calculate the mole fraction of each component of a gas mixture.

nO2

nt=

5.0 mol

20.0 mol= 0.25

Partial Pressure

• The partial pressure of a gas in a mixture can be found:

PA = XA Ptotal

where PA = partial pressure of gas A

XA = mole fraction of gas A

Ptotal = total pressure of mixture

Example of Partial Pressure Calculation

A mixture of gases contains 0.51 mol N2, 0.28 mol H2, and 0.52 mol NH3. If the total pressure of the mixture is 2.35 atm, what is the partial pressure of H2?

PH2 = XH2

Ptotal

XH2=

0.28 mol0.28 mol + 0.51 mol + 0.52 mol

= 0.21

PH2= 0.21 x 2.35 = 0.50 atm

Dalton’s law of Partial PressureThe simple gas laws and idea gas law apply to individual gases as well as to a mixture of nonreactive gases. What is responsible for the pressure in a gas mixture? Since the pressure of pure gas at constant V and T is proportional to its amount (P=nRT/V), the pressure contribute from each individual gas in a mixture is also its amount in the mixture.

In other words, the total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the partial pressure of each individual gas in the container, a statement known as Dalton’s law of partial pressure

Ptot = PA + PB+ PC….at constant V and T

Where PA, PB, PC …. refer to the pressure of each individual gas would have if it

was alone.

→usually referred to as the “vapor pressure”

NOTE: In McConkey textbook, the subscript “v” is represented by subscript “s”

**Throughout this chapter, the subscript “a” denotes dry air and the subscript “v” denotes water vapor**

At temperatures below 50oC,the enthalpy of water vapor in air can be taken to be equal to the enthalpy of saturated vapor at the same temperature. That is,

Eq. (14.4)

-The amount of water vapor in the air can be specified in various ways.

-Probably the most logical way is to specify directly the mass of water vapor presentin a unit mass of dry air, that is called absolute or specific humidity (or humidity ratio)

NOTES:

NOTE: In McConkey textbook, the subscript “v” is represented by subscript “s”

-The amount of moisture in the air has a definite effect on how comfortable we feel in an environment.

-However, the comfort level depends more on the relative humidity.

What is saturated air?..

Consider 1 kg of dry air. Specific humidity is zero. Now let us add some water vapor tothis dry air. The specific humidity will increase. As more vapor or moisture is added,the specific humidity will keep increasing until the air can hold no more moisture. At thispoint, the air is said to be saturated with moisture, and it is called saturated air.

*For 1 kg of dry air

Relative humidity also can be expressed as,

since

22

ADIABATIC SATURATION AND WET-BULB TEMPERATURES

The adiabatic saturation process and its representation on a T-s diagram of water.

The specific humidity (and relative humidity) of air can be determined from these equations by measuring the pressure and temperature of air at the inlet and the exit of an adiabatic saturator.

Psychrometer

- Two thermometers available in the psychrometer.

- One of them indicates the air temperature andis called the dry bulb thermometer.

- The bulb of the second is surrounded by a wickwhich dips into a small reservoir of water and airflow over the wick , and the temperature indicated is called the wet bulb temperature.

Continuity of Previous Example..Example 14-6

Air enters a window air conditioner at 1 atm, 30oC and 80% relative humidity, and leaves as

saturated air at 14oC. By using psychrometric chart,

i) Show the process path on the chart

ii) determine the amount of moisture that is removed from the air due to condensation, kg

H2O/kg dry air

iii) determine initial enthalpy of the air, kJ/kg dry air

iv) determine final enthalpy of the air, kJ/kg dry air

v) determine the heat rejected from the air during this process , kJ/kg dry air

EXAMPLE 14-2 Fogging of the Windows in a House

In cold weather, condensation frequently occurs on the inner surfaces of the windowsdue to the lower air temperatures near the window surface. Consider a house that containsair at 20oC and 75percent relative humidity. At what window temperature will themoisture in the air start condensing on the inner surfaces of the windows?