1. Objectives Describe psychrometric quantities Given any two psychrometric quantities, calculate any other quantity Use Tables A4 or psychrometric charts to look up psychrometric quantities Calculate psychrometric quantities at non- standard conditions Evaluate psychrometric processes (8.1-8.4)

2. 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

3. 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

4. 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

5. Wet-bulb temperature, t* 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

6. 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

8. 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)

9. Ref: Tao and Janis (2001)

13. Examples What is enthalpy of air in the classroom right now? Condensation on windows when taking a shower How cold does it have to be outside for condensation to form on windows? –Assumption is that windows are the same temperature as outside air –80 °F, RH = 80%

15. 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

16. A diversion… For an ideal gas, h a = ∫c pa dT, h w = ∫c pw dT So, h a = c pa 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 pa t + W(c pw t + h g0 ) h = c p t + W∙h g0, c p = c pa + 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

17. Approximating Psychrometric Processes Δh s = c p Δt, Δh L = h w ΔW=(c pw t + h g0 ) ΔW Where do these come from? Δh = h 2 – h 1, Δt = t 2 – t 1, ΔW = W 2 – W 1, t = (t 1 + t 2 )/2, W = (W 1 + W 2 )/2 Δh = Δh s + Δh L Major result Δh s = c p Δt, Δh L = h w ΔW

18. Summary Describe psychrometric quantities Given any two psychrometric quantities, calculate any other quantity Use Tables A4 or psychrometric charts to look up psychrometric quantities Calculate psychrometric quantities at non- standard conditions

19. Psychrometric Processes Adiabatic mixing of two streams Sensible heating and cooling Dehumidification by cooling Humidification Evaporative cooling

20. Adiabatic mixing Governing equation

21. Sensible heating

22. Dehumidification by Cooling