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

Units Pound mass and pound force Acceleration due to gravity lbm = lbf (on Earth, for all practical purposes) Acceleration due to gravity g = 9.807 m/s2 = 32.17 ft/s2 Pressure (section 2.5 for unit conversions) Temperature (section 2.6 for unit conversions)

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

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

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

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)

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

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)

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)

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

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 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)

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

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

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

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

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