Thermodynamic

🔑 Key Thermodynamic Properties You Should Know

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Specific Humidity (γ) — The Moisture Pie 🍰

A friendly, visual way to see how much of the total air mass is actually water vapor.

Alright, let’s continue our journey into the moist world of air! 😄 You already know that the humidity ratio (W) tells us how much water vapor exists per kilogram of dry air. But what if you’re not just interested in dry air… what if you want to know: “Out of the whole chunk of air — both dry and moist — how much of it is actually water vapor?”

That’s where Specific Humidity (γ) comes in. It gives us the water vapor as a slice of the total air mass pie. 🥧

Definition. Specific Humidity (γ) is the mass of water vapor divided by the total mass of moist air (dry air + water vapor).

Formula (from ASHRAE Fundamentals)

gamma = Mw/(Mw + Mda)

Where: Mw = mass of water vapor, Mda = mass of dry air.

Shortcut if you already know W
If you know the humidity ratio (W = Mw/Mda), then γ = W / (1 + W). Conversely, W = γ / (1 − γ).
0.00% of total mass is H₂O

This donut shows γ as a percentage of the total air mass.

Interactive: Convert Between Humidity Ratio (W) and Specific Humidity (γ)

Cross‑check using the base definition (Mw & Mda)

Let’s Break It Down with a Story

Picture a balloon filled with air 🎈. It contains 1.00 kg of dry air and 0.020 kg of water vapor.

  • Total air mass = 1.000 + 0.020 = 1.020 kg
  • W = 0.020 / 1.000 = 0.0200
  • γ = 0.020 / 1.020 = 0.0196 (≈ 1.96% of total mass)

Neat, right? γ tells you the share of water vapor in the whole air mixture.

📎 Citation

ASHRAE Fundamentals Handbook, Chapter 1 — Psychrometrics. Definition of specific humidity and relation to humidity ratio.

If you’re prepping for design calcs, keep this relation handy: γ = W/(1+W).

Relative Humidity (φ) — Why Air Feels Damp or Dry 🧂💦

It’s not just temperature — it’s how full the air is with moisture.

So you’ve walked into a room and said, “Ugh, it feels humid in here…” or maybe “This dry air is killing my skin!” 😩 That feeling? Relative Humidity (φ). It tells you how close the air is to being full of moisture.

Think sponge: If the air is holding half the moisture it can, φ ≈ 50%. If it’s fully soaked, φ = 100% (dew point reached, condensation starts). If it’s barely holding any, φ ≈ 10%.

ASHRAE‑Approved Definition

phi = pw/pws
φRelative humidity (decimal or %)
pwPartial pressure of water vapor (kPa)
pwsSaturation vapor pressure at dry‑bulb temperature t (kPa)

For most HVAC jobs this simplified form is accurate and easy.

High‑accuracy version (labs & metrology)
phi = f(p,td)e(td) / (f(p,t)e(t))

Uses enhancement factor f and accurate e(t) correlations. In typical building work, φ ≈ e(Td)/e(T).

0% feels comfy

Donut shows φ; sponge fill rises as humidity increases.

Calculate φ — Two Easy Ways

If provided, φ ≈ e(Td)/e(T). Also returns φ‑based dew point.

Why φ Matters (and Changes with Temperature)

φ = 100% means any extra moisture condenses: dew on surfaces, fog, sticky skin, condensate on AC coils. φ falls when air warms (can hold more vapor) and rises when air cools (capacity drops). That’s why winter air feels dry and post‑rain summer air feels muggy.

Example (25 °C with ASHRAE Table 3)

Measured pw=2.50 kPa and pws(25 °C)=3.17 kPa → φ = 2.50/3.17 = 0.78978.9%. Feels a bit sticky 🥵.

📎 Citations

ASHRAE Fundamentals Handbook, Chapter 1 — Psychrometrics (Table 3, Eqns). Saturation pressures and RH definitions. Images: pw/pws and advanced φ from site assets.

Enthalpy (h) — The Total Heat Story of Moist Air

Your one‑stop number for both sensible and latent heat in HVAC design.

Enthalpy is like a heat energy scorecard for moist air. It tells you the total heat in 1 kg of dry air plus its associated water vapor. That includes the heat due to temperature (sensible) and the hidden heat stored in water vapor (latent).

TypeWhat it isExample
🌡️ Sensible heatHeat due to air temperatureAir gets warmer or cooler
💧 Latent heatEnergy stored in water vaporEvaporating/condensing moisture

ASHRAE’s Working Equation

h = 1.006·t + W·(2501 + 1.86·t)  [kJ/kgda],   t in °C, W in kg/kgda

  • h: specific enthalpy of moist air
  • 1.006: cp of dry air (kJ/kg·K)
  • 2501: latent heat of vaporization at 0 °C (kJ/kg)
  • 1.86: cp of water vapor (kJ/kg·K)

Sensible vs latent contribution appears after calculation.

Calculate h

Two‑State Process — Δh and Power

Compare two conditions and estimate required heating/cooling power. Density from ideal dry‑air equation.

📎 Citations

ASHRAE Fundamentals Handbook, Chapter 1 — Psychrometrics. Standard moist‑air enthalpy equation and property tables (incl. negative h at low T). Psychrometric charts show h as slanted lines.

Psychrometric Chart (for context)

Psychrometric chart excerpt with enthalpy lines

Enthalpy lines slope upward; moving along them changes moisture at nearly constant h when adiabatic saturation occurs.

Thermodynamic Wet‑Bulb and Dew‑Point Temperatures — The Hidden Truths in the Air

Unlock comfort and condensation: dew‑point tells you when air condenses, wet‑bulb tells you how far evaporation can cool it.

Ever wondered why sweating works great in dry weather but feels sticky in the tropics? Or why your car is beaded with dew at sunrise? These everyday moments have names in HVAC: dew‑point temperature and thermodynamic wet‑bulb temperature. Master these and you unlock serious air‑handling power. 🔓

What Is Dew‑Point Temperature (td)?

It’s the temperature where moist air hits 100% RH and water begins to condense. Dip below it → fog, dew, sweat that won’t evaporate.

ASHRAE definition. td is the temperature where the actual humidity ratio W equals the saturation humidity ratio at the same pressure: W = Ws(p, td).
W = Ws(p, td)

Given W and p, solve for td. Equivalently, compute pw and find T where pws(T)=pw.

pws(td)=p_w = p*W/(0.621945+W)

Thermodynamic Wet‑Bulb Temperature (t*)

The temperature at which water evaporates into air adiabatically to bring the air to saturation at the same T and p. It’s the theoretical limit of evaporative cooling.

In equations, we solve for t* by balancing enthalpy of the initial air with the saturated state at t* (see calculator).

Compute Dew‑Point (td) & Thermodynamic Wet‑Bulb (t*)

Saturation pressure pws(T) auto‑computed via equation.
φ 0% status

Why They Matter

  • Dew‑point predicts condensation on ducts, glazing, and coils.
  • Wet‑bulb sets the limit for evaporative coolers and shows how far air can be cooled by adiabatic humidification.
  • At constant moisture, warming air lowers φ; cooling raises φ — same vapor, different capacity.

📎 Citations

ASHRAE Fundamentals Handbook, Chapter 1 — Psychrometrics. Dew‑point definition (W = Ws(p,td)), vapor pressure relation pw=p·W/(0.621945+W), and thermodynamic wet‑bulb via enthalpy balance. Images from site assets are highlighted above.

Compression Refrigeration Cycles — How We Make Things Cool!

The vapor‑compression cycle is the quiet rockstar inside fridges, ACs, chillers, heat pumps — even ice‑cream machines 🍦.

Ever wonder how your air conditioner chills your room in a heatwave or how a refrigerator stays frosty while the kitchen roasts? It’s one magical thermodynamic loop: the vapor‑compression refrigeration cycle. In simple words, it’s a closed loop that picks up heat from a cool space and dumps it outside. That seems backward (cold → hot), so we “cheat” nature by adding mechanical work with a compressor. 💪

Compressor 1 → 2 Condenser 2 → 3 Expansion Valve 3 → 4 Evaporator 4 → 1 1→2 2→3 3→4 4→1 T₀ Q₃ Tᵣ Q₁ W₂
Q₁: Heat absorbed (evaporator) Q₃: Heat rejected (condenser) W₂: Compressor work

Low‑pressure vapor enters the compressor (1→2). Work raises pressure & temperature; it leaves as hot, high‑pressure vapor.

The 4 Core Components

#ComponentFunctionPhase
1️⃣CompressorRaises P & T (adds work)Vapor → hotter vapor
2️⃣CondenserRejects heat to ambientVapor → liquid
3️⃣Expansion DeviceDrops pressure/temperatureLiquid → cold mix
4️⃣EvaporatorAbsorbs heat from spaceMix → vapor

Refrigerant example: R‑134a. The loop repeats continuously. 🔁

Step‑by‑Step Walkthrough

1 → 2: The Compressor (Power Booster)
Cold, low‑pressure vapor enters. The compressor squeezes it to a hot, high‑pressure vapor. Work input W₂ drives the whole cycle.

2 → 3: The Condenser (Heat Dumper)
Hot vapor releases heat Q₃ to air/water at T₀ and condenses to a high‑pressure liquid.

3 → 4: The Expansion Valve (Pressure Dropper)
Liquid flashes across a restriction, dropping in pressure and temperature — producing a cold liquid‑vapor mix.

4 → 1: The Evaporator (Heat Soaker)
The cold mix absorbs heat Q₁ from the cooled space at Tᵣ, fully evaporating back to vapor and returning to the compressor. Boom — cooling achieved.

How Efficient Can It Be? (COP Upper‑Bound)

COPR,Carnot = Te / (Tc − Te)   with T in Kelvin

Bars are scaled with W set to 1 unit: Q₁ = COP·W, Q₃ = Q₁ + W.

Pro Tips: Superheat & Subcooling (Why Techs Care)

  • Superheat (exit of evaporator): ensures only vapor enters the compressor — protects against liquid slugging.
  • Subcooling (exit of condenser): ensures liquid reaches the expansion device — improves capacity.

Classic Textbook Schematic (for reference)

Classic vapor compression cycle schematic with Q1, Q3 and W2 arrows
Click to open full‑size. Labels match the interactive diagram above.

Multistage Vapor Compression Systems — Why One Compressor Isn’t Always Enough

When you push for ultra‑low temps (blast freezers, vaccine storage, ice rinks), splitting compression into stages keeps ratios sane, temperatures lower, and efficiency up.

Why Go Multistage?

  • High compression ratio at very low evaporating temperatures → punishing discharge temps.
  • Poor COP when one stage does all the work.
  • Reliability: sharing the lift between stages reduces stress on each compressor.

Solution: compress in steps and cool the vapor in between with a flash intercooler / economizer.

Low‑Stage Compressor (1→2) Flash Intercooler High‑Stage Compressor (3a→4) Condenser 4→5 Evaporator 5→1 1 2 3a 4 5 → to flash 5→evap valve cold liquid to 5→1
Low‑Stage: 1→2 Flash Intercooler splits vapor (3a) & liquid (3b) High‑Stage: 3a→4 Condenser: 4→5 Evaporator: 5→1

1→2: Low‑stage compressor lifts vapor to intermediate pressure; vapor goes to the flash tank.

The Flow: Two‑Stage with Flash Intercooling

  1. Low‑Stage Compressor (1→2): Raises pressure from evaporator to intermediate.
  2. Flash Intercooler (2→3a & 3b): A portion of liquid from the condenser is expanded here. Flash vapor cools the stream; separator sends vapor → high‑stage and cold liquid → evaporator.
  3. High‑Stage Compressor (3a→4): Compresses the cooled vapor to condensing pressure.
  4. Condenser (4→5): Rejects heat, then splits: some liquid to intercooler, the rest to the evaporator’s expansion device.
  5. Evaporator (5→1): Cold liquid flashes and absorbs heat from the load, returning as vapor.

Single vs Two‑Stage — Quick Work & Discharge Temperature Comparison

Educational, ideal‑gas style estimate using cp and k. Defaults are typical for R‑134a vapor near 0–40 °C. Intercooler assumes vapor is cooled back to the low‑stage inlet temperature.

Tip: try √(Pe·Pc) for near‑optimal staging. With the defaults: √(80·1000) ≈ 283 kPa.

Zeotropic vs. Azeotropic Refrigerant Mixtures — Not All Liquids Boil the Same 🔥💨

Some blends act like one fluid. Others “glide” as they boil/condense. Understand the difference and design smarter systems.

Refrigerants are the lifeblood of cooling systems — evaporating, condensing, and looping forever. Some are pure fluids; some are blends. And blends come in two personalities:

Azeotropic → acts like one fluid Zeotropic → components boil/condense over a range (glide)

🧠 First, What Is a Refrigerant Mixture?

A combo of two or more pure fluids (e.g., R-32 + R-125) behaving as one refrigerant. How they phase-change defines their category:

TypeBehavior
AzeotropicBoils/condenses at constant temperature; behaves like a single fluid
ZeotropicBoils/condenses over a temperature range; has glide

Examples

  • Zeotropic / near-azeotropic: R-407C, R-404A, R-410A (very small glide)
  • Azeotropic: R-500, R-502, and newer low-GWP blends formulated to be near-azeotropic

🌡️ Temperature Glide — Why It Matters

Glide is the difference between the bubble point (boiling begins) and the dew point (boiling ends). In zeotropes, both evaporation and condensation occur across that range — not at a flat temperature.

FeatureZeotropicAzeotropic
Temp glideYesNo
Heat-exchanger designMust account for varying TEasier
Fractionation riskYesNo
ChargingLiquid onlyVapor or liquid
EfficiencyCan be higher if glide matches HX profileStable across temps

🎛️ Glide Visualizer (with LMTD)

Toy model of a condenser. Adjust glide and secondary-fluid temps to see how the driving force changes. When glide “lines up” with the other stream, the minimum ΔT (pinch) improves — boosting LMTD.

Temp (°C) Heat-exchanger length →

🚨 Fractionation & Charging

In zeotropes, components have different volatilities. If the system leaks vapor, composition drifts — properties shift and performance changes. Always charge zeotropes as liquid to keep the blend ratio correct.

Charging tip: Liquid charging for zeotropes; vapor or liquid works for azeotropes.

⚙️ System Design — Where Each Shines

ApplicationOften PreferredWhy
Residential ACNear-azeotropic (e.g., R-410A)Very small glide, stable performance
Industrial chillersAzeotropicSimplicity, predictable control
Low-GWP transitionsMany zeotropic blendsBalancing properties & regulations
Long HX / temperature-matchZeotropicGlide can boost LMTD when matched

🧪 Quick Quiz

1) A blend that boils at a constant temperature is…
2) With zeotropes, field charging should be done as…
3) Temperature glide can increase HX effectiveness when…

📎 Citations

ASHRAE Fundamentals Handbook, Chapter 2 — Refrigerants. Guidance on zeotropic/azeotropic behavior, temperature glide, fractionation risk, and charge practices. (Highlights summarized; use manufacturer data for exact glide and charging procedures.)

Comparison of Azeotropic vs Zeotropic Refrigerant Blends

Search, filter, sort, and visualize temperature glide. Values are indicative — always check current data sheets.

Refrigerant Blend Type Glide (°C) Description

Charging tip Zeotropic & near-azeotropic blends should be charged as liquid (to avoid fractionation). Azeotropic & pure fluids can be charged as liquid or vapor.

ASHRAE Fundamentals, Ch. 2 — Refrigerants: defines azeotropic/zeotropic behavior, temperature glide, and charging practices. Use manufacturer data for exact glides.

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