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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 Δ u = c v Δ t Δ h = c p Δ t c p - c v = R.

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Announcements

Announcements

  • Tonight ASHRAE Student Chapter Meeting


Objectives

Objectives

  • Finish with review thermodynamics

  • Learn about Psychrometrics


P h diagram

p-h diagram


Ideal gas law

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

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

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)

PxV = mx Rx∙T

PyV = 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 constant

T = absolute temperature (K, °R)


Mass weighted averages

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

Properties of water

  • Water, water vapor (steam), ice

  • Properties of water and steam (pg 675 – 685)

    • Alternative - ASHRAE Fundamentals ch. 6


Humidity ratio w

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 saturation

ma = mass of dry air

mw = mass of water vapor


Relative humidity

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

x = mole fraction

P = pressure

μ = degree of saturation

W = humidity ratio


Dew point temperature t d

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

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 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

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

Alternate calculation for W

  • PV = mRT (IGL)

  • What do we know about R ratio?

  • P = Pw + Pa

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

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 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

Adiabatic mixing

  • Governing equation

External heat


Sensible heating

Sensible heating


Dehumidification by cooling

Dehumidification by Cooling


Real dehumidification process

Real Dehumidification Process


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