Thermodynamics
Core framework
The First Law is the backbone: for a closed system, Q − W = ΔU; for a steady-flow open system, q − w = Δh + Δke + Δpe. Because HVAC equipment is almost always open flow, work with enthalpy, not internal energy. Recall h = u + Pv, and for ideal gases Δh = cpΔT while Δu = cvΔT, with cp − cv = R and k = cp/cv.
Second Law and cycles
The Carnot COP between reservoirs at absolute temperatures TL and TH is COP_R = TL/(TH − TL) for refrigeration and TH/(TH − TL) for a heat pump. Real cycles approach, never reach, this. Isentropic efficiency compares actual work to ideal work for compressors (η_c = (h2s − h1)/(h2 − h1)) and expansion devices are modeled as isenthalpic (h constant) throttling processes - not isentropic.
Traps that appear in questions
- Using gauge pressure in a saturation table lookup.
- Using °F instead of °R in the Carnot relation.
- Forgetting that hot and cold stream energy balances (ṁ cp ΔT) must be set equal in an adiabatic heat exchanger.
- Confusing a mixing process (adiabatic, energy-conserving, entropy-generating) with a work-producing process.
- Assuming ideal-gas behavior near saturation.
Worked example
A chiller evaporates at 40°F and condenses at 100°F. TL = 500 °R, TH = 560 °R, so Carnot COP = 500/(560 − 500) = 8.33. A real machine at roughly half the Carnot value delivers COP ≈ 4.2. That "fraction of Carnot" check is a fast way to sanity-check any cycle answer.