1. Objectives
Solve thermodynamic problems and use properties in equations (today)
Calculate heat transfer by all three modes including phase change (Thursday)
Apply Bernoulli equation to flow in a duct and use a pitot tube (Tuesday)
Differentiate heat exchangers (Tuesday)
Used prometheus

2. Units Pound mass and pound force Acceleration due to gravity
lbm = lbf (on Earth, for all practical purposes)
Acceleration due to gravity
g = m/s2 = ft/s2
Pressure (section 2.5 for unit conversions)
Temperature (section 2.6 for unit conversions)

3. Thermodynamic Properties
ρ = density = mass / volume
v = specific volume = 1 / ρ
specific weight = weight per unit volume (refers to force, not to mass)
specific gravity = ratio of weight of volume of liquid to same volume of water at std. conditions (usually 60 °F or 20 °C)
Both functions of t, P

4. Heat Units
Heat = energy transferred because of a temperature difference
Btu = energy required to raise 1 lbm of water 1 °F kJ
Specific heat (heat per unit mass)
Btu/(lbm∙°F), kJ/(kg∙°C)
For gasses, two relevant quantities cv and cp
Basic equation (2.10) Q = mcΔt
Q = heat transfer (Btu, kJ)
m = mass (kg, lbm)
c = specific heat
Δt = temperature difference

5. Sensible vs. latent heat
Sensible heat Q = mcΔt
Latent heat is associate with change of phase at constant temperature
Latent heat of vaporization, hfg
Latent heat of fusion, hfi
hfg for water (100 °C, 1 atm) = 1220 Btu/lbm
hfi for ice (0 °C, 1 atm) = 144 Btu/lbm

6. Work, Energy, and Power
Work is energy transferred from system to surroundings when a force acts through a distance
ft∙lbf or N∙m (note units of energy)
Power is the time rate of work performance
Btu/hr or W
Unit conversions in Section 2.7
1 ton = 12,000 Btu/hr (HVAC specific)

7. Thermodynamic Laws First law? Second law? Implications for HVAC
Need a refrigeration machine (and external energy) to make energy flow from cold to hot

8. Internal Energy and Enthalpy
1st law says energy is neither created or destroyed
So, we must be able to store energy in a fluid
Internal energy (u) is all energy stored
Molecular vibration, rotation, etc.
Formal definition in statistical thermodynamics
Enthalpy
Composite energy (sensible + latent)
We always track this term in HVAC analysis
h = u + Pv
h = enthalpy (J/kg, Btu/lbm)
P = Pressure (Pa, psi)
v = specific volume (m3/kg, ft3/lbm)

9. Entropy Not directly measurable Mathematical construct
Reversible process
Note difference between s and S
Entropy can be used as a condition for equilibrium
What do enthalpy, internal energy, and entropy all have in common?
S = entropy (J/K, BTU/°R)
Q = heat transfer (J, BTU)
T = absolute temperature (K, °R)

10. T-s diagrams dh = Tds + vdP (general property equation)
Area under T-s curve is change in specific enthalpy – under what condition?

11. 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)

12. 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∙T
Py 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 constant
T = absolute temperature (K, °R)

13. Enthalpy of perfect gas mixture
Assume adiabatic mixing and no work done
What is mixture enthalpy?
What is mixture specific heat (cp)?

14. Properties of water Water, water vapor (steam), ice
Properties of water and steam (pg 675 – 685)
Alternative - ASHRAE Fundamentals ch. 6

15. Quality Quality, x, is mg/(mf + mg)
Vapor mass fraction
ζ = v or h or s in expressions below
ζ = ζf + x ζfg
ζ = (1- x) ζf + x ζg
ζ = ζg - (1- x) ζfg
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 latent heat of vaporization

16. Thermodynamic Properties Refrigerants
What is a refrigerant?
Usually interested in phase change
What is a definition of saturation?
Enthalpy of liquid is ~the same as saturated liquid at same temperature
ASHRAE Fundamentals ch. 20 is more complete reference than your text

17. Homework Assignment 1 Review material from chapter 2
Mostly plug and chug
Depends on your memory of thermodynamics and heat transfer
You should be able to do any of problems in Chapter 2
Problems 2.2, 2.6, 2.10, 2.12, 2.14, 2.20, 2.22, 2.16a
Due on Thursday 9/15