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 = c v Δt Δh = c p Δt c p - c v = R M = molecular weight (g/mol, lbm/mol) P = pressure (Pa, psi) V = volume (m 3, ft 3 ) v = specific volume (m 3 /kg, ft 3 /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 = m x m y V = V x V y T = T x T y P = P x P y Assume air is an ideal gas -70 °C to 80 °C (-100 °F to 180 °F) P x V = m x R x ∙ T P y V = m y R y ∙ T What is ideal gas law for mixture? m = mass (g, lbm) P = pressure (Pa, psi) V = volume (m 3, ft 3 ) R = material specific gas constant T = absolute temperature (K, °R)

Mass-Weighted Averages Quality, x, is m g /(m f + m g ) Vapor mass fraction φ= v or h or s in expressions below φ = φ f + x φ fg φ = (1- x) φ f + x φ g s = entropy (J/K/kg, BTU/°R/lbm) m = mass (g, lbm) h = enthalpy (J/kg, Btu/lbm) v = specific volume (m 3 /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 = m w /m a Degree of saturation, µ = W/W s Humidity ratio is hard to measure, but very useful in calculations What are units? Is W a function of temperature? What about W s ? W s = humidity ratio at saturation m a = mass of dry air m w = mass of water vapor

Relative Humidity Φ = x w /x w,s = P w /P ws Function of T Easy to measure and useful in some contexts, but often need to know temperature as well x = mole fraction P = pressure μ = degree of saturation W = humidity ratio

Dew-point temperature, t d Temperature at which condensation will form Under appropriate surface conditions Vapor is saturated Φ = ? W s (P, t d ) = 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 W s for calculations Subscripts: a = dry air, s = saturated air v = v a +µv as h = h a +µh as s = s a +µs as

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 = P w + P a R = gas constant P = pressure V = volume T = absolute temperature W = humidity ratio Subscripts: w is water vapor, a is dry air

Calculation of psychometric quantities For an ideal gas, h da = ∫c pa dT, h w = ∫c pw dT So, h da = c p,da t which assumes a reference state of 0 °F or 0 °C – Tables A4 Note different reference h w = c pw t + h g0 h = c p,da t + W(c pw t + h g0 ) Or you can use: h = c p t + W∙h g0, c p = c p,da + Wc pw c p = specific heat h = enthalpy T = absolute temperature t = temperature W = humidity ratio Subscripts: w is water vapor, a is dry air, g is saturated water vapor

Adiabatic mixing Governing equation External heat

Sensible heating

Dehumidification by Cooling

Real Dehumidification Process