Announcements

• Tonight ASHRAE Student Chapter Meeting

Objectives

• Finish with review thermodynamics

• Learn about Psychrometrics

p-h diagram

Ideal gas law

• Pv = RT or PV = nRT • R is a constant for a given fluid

• For perfect gasses• Δu = cvΔt

• Δh = cpΔt

• cp - cv= R

KkgkJ314.8

Rlbf

lbmft1545

MMR

M = molecular weight (g/mol, lbm/mol)P = pressure (Pa, psi)V = volume (m3, ft3)v = specific volume (m3/kg, ft3/lbm)T = absolute temperature (K, °R)t = temperature (C, °F)u = internal energy (J/kg, Btu, lbm)h = enthalpy (J/kg, Btu/lbm)n = number of moles (mol)

Mixtures of Perfect Gasses

• m = mx my

• V = Vx Vy

• T = Tx Ty

• P = Px Py

• Assume air is an ideal gas• -70 °C to 80 °C (-100 °F to 180 °F)

Px V = mx Rx∙TPy V = my Ry∙T

What is ideal gas law for mixture?

m = mass (g, lbm)P = pressure (Pa, psi)V = volume (m3, ft3)R = material specific gas constantT = absolute temperature (K, °R)

Mass-Weighted Averages

• Quality, x, is mg/(mf + mg)• Vapor mass fraction

• φ= v or h or s in expressions below• φ = φf + x φfg

• φ = (1- x) φf + x φg

s = entropy (J/K/kg, BTU/°R/lbm)m = mass (g, lbm)h = enthalpy (J/kg, Btu/lbm)v = specific volume (m3/kg)

Subscripts f and g refer to saturated liquid and vapor states and fg is the difference between the two

Properties of water

• Water, water vapor (steam), ice• Properties of water and steam (pg 675 – 685)

• Alternative - ASHRAE Fundamentals ch. 6

Humidity Ratio, W

• W = mw/ma

• Degree of saturation, µ = W/Ws

• Humidity ratio is hard to measure, but very useful in calculations

• What are units?• Is W a function of temperature? What about

Ws? Ws = humidity ratio at saturationma = mass of dry airmw = mass of water vapor

Relative Humidity

• Φ = xw/xw,s = Pw/Pws

• Function of T

Easy to measure and useful in some contexts, but often need to know temperature as well

WWs

622.0622.0

x = mole fractionP = pressureμ = degree of saturationW = humidity ratio

Dew-point temperature, td

• Temperature at which condensation will form• Under appropriate surface conditions

• Vapor is saturated• Φ = ?• Ws(P, td) = W

Wet-bulb temperature, VBT (t*)• Temperature of wet surface or

• Temperature at which water, by evaporating into the air, will bring air to saturation adiabatically

• * superscript is designation that variable is evaluated at the wet-bulb temperature

• Note, distinct from that measured by a sling psychrometer• Section 9.5

Tables for Moist Air (P = 1 atm)

• Tables A.4 in your text• Ability to get Ws for calculations• Subscripts:

• a = dry air, s = saturated air

v = va+µvas

h = ha+µhas

s = sa+µsas

Psychrometric Chart

• Need two quantities for a state point• Can get all other quantities from a state point

• Can do all calculations without a chart• Often require iteration• Many “digital” psychrometric charts available

• Can make your own• Best source is ASHRAE fundamentals (Chapter 6)

• Also in your text (back cover fold-out)

Alternate calculation for W

• PV = mRT (IGL)

• What do we know about R ratio?• P = Pw + Pa

w

a

a

w

TRVPTRVP

a

wRR

PP

mmW

a

a

w

w

w

wPP

PW

622.0

R = gas constantP = pressureV = volumeT = absolute temperatureW = humidity ratio

Subscripts: w is water vapor, a is dry air

Calculation of psychometric quantities

• For an ideal gas,• hda = ∫cpadT, hw = ∫cpwdT

• So, hda = cp,dat which assumes a reference state of 0 °F or 0 °C – Tables A4• Note different reference

• hw = cpwt + hg0

• h = cp,dat + W(cpwt + hg0)Or you can use:• h = cpt + W∙hg0, cp = cp,da + Wcpw

cp = specific heath = enthalpyT = absolute temperaturet = temperature W = humidity ratio

Subscripts: w is water vapor, a is dry air, g is saturated water vapor

Adiabatic mixing

• Governing equation hmQhmoutin

External heat

Sensible heating

tcmQ p

Dehumidification by Cooling

Real Dehumidification Process