2.4 Gas Laws Applied to HVAC/R Systems
Key Takeaways
- Thermodynamic gas laws strictly require absolute temperature measured in Rankine (°R = °F + 459.67) or Kelvin (K = °C + 273.15); calculating with customary Fahrenheit yields invalid answers.
- Absolute pressure (psia) equals gauge pressure (psig) plus atmospheric barometric pressure (14.7 psi at sea level); deep vacuum is quantified in microns of mercury (25,400 microns = 1 in. Hg).
- Boyle's Law (P1 · V1 = P2 · V2) governs compressor displacement and compression ratios, establishing that halving vapor volume doubles its absolute pressure at constant temperature.
- Charles's Law (V1 / T1 = V2 / T2) and Gay-Lussac's Law (P1 / T1 = P2 / T2) explain nitrogen holding pressure variations during ambient temperature swings and refrigerant cylinder thermal expansion.
- Dalton's Law of Partial Pressures dictates that total pressure is the sum of all individual gas partial pressures; non-condensable air trapped in a refrigeration circuit directly increases head pressure, reduces subcooling accuracy, and elevates compressor power consumption.
2.4 Gas Laws Applied to HVAC/R Systems
[!NOTE] Gas Law Foundations in HVAC/R Systems: All vapor-compression refrigeration circuits, fuel gas combustion systems, pneumatic controls, and nitrogen testing procedures are governed by physical gas laws. Gaseous refrigerants, natural gas, propane, air, and nitrogen expand, contract, exert pressure, and absorb energy according to predictable mathematical relationships between pressure, volume, temperature, and molecular density. Understanding these principles is essential for field diagnostics and passing the Arkansas licensing exam.
Absolute Temperature and Pressure Scales
A critical requirement for solving any thermodynamic gas law equation is that all calculations must be performed using absolute temperature and absolute pressure scales. Utilizing standard gauge pressure (psig) or customary Fahrenheit temperatures (°F) directly in gas equations yields mathematically incorrect results.
Absolute Temperature Scales: Rankine and Kelvin
Ordinary temperature scales (Fahrenheit and Celsius) are referenced to the freezing and boiling points of water. However, thermal molecular motion does not cease at 0°F or 0°C. Molecular motion ceases entirely only at Absolute Zero ($-459.67^\circ\text{F}$ or $-273.15^\circ\text{C}$).
- The Rankine Scale ($^\circ\text{R}$): The absolute thermodynamic temperature scale corresponding to the Fahrenheit system:
- The Kelvin Scale ($K$): The absolute thermodynamic temperature scale corresponding to the Celsius system:
Rule of Practice: If an exam problem states that gas inside a cylinder is heated from 40°F to 80°F, the temperature has not doubled. In absolute terms, the temperature has only increased from $500\text{ R}$ ($40 + 460$) to $540\text{ R}$ ($80 + 460$), a modest increase of 8%.
Absolute Pressure vs. Gauge Pressure
Pressure is defined as force applied perpendicular to a surface per unit area ($P = F / A$). In the U.S. Customary system, pressure is measured in pounds per square inch (psi).
- Atmospheric Pressure ($P_{\text{atm}}$): The weight of the Earth's atmosphere exerting force on the Earth's surface. At sea level under standard temperature conditions (59°F), atmospheric pressure equals $14.696\text{ psia} \approx 14.7\text{ psia}$ (or $29.921\text{ inches of mercury}$). Atmospheric pressure decreases with increasing altitude.
- Gauge Pressure (psig): Pressure measured relative to local atmospheric pressure. A standard manifold gauge reads $0\text{ psig}$ when open to the atmosphere.
- Absolute Pressure (psia): Pressure measured relative to a perfect, complete vacuum (0 psia):
+-------------------------------------------------------------+ 114.7 psia (100 psig)
| |
| GAUGE PRESSURE (psig) |
| |
+=============================================================+ 14.7 psia (0 psig - Atmospheric Baseline)
| VACUUM RANGE (in. Hg) |
+-------------------------------------------------------------+ 0 psia (-29.92 in. Hg / 0 Microns / Absolute Zero)
Vacuum Measurement: Inches of Mercury and Microns
Pressures below atmospheric pressure fall into the vacuum range:
- Inches of Mercury Vacuum (in. Hg vac): Standard Bourdon tube manifold gauges measure vacuum from $0\text{ in. Hg}$ (atmospheric) down to $-29.92\text{ in. Hg}$ (perfect vacuum).
- The Micron: Mechanical dial gauges lack the sensitivity needed to verify deep evacuation. Technicians use electronic digital vacuum gauges calibrated in microns (one millionth of a meter of mercury column height, or $0.001\text{ mm Hg}$):
The Classical Gas Laws in HVAC/R Systems
1. Boyle's Law: Pressure-Volume Relationship (Constant Temperature)
Formulated by Robert Boyle in 1662, Boyle's Law states that the absolute pressure of a given mass of gas is inversely proportional to its volume, provided the temperature remains constant within a closed system.
If the volume occupied by a gas is halved, its absolute pressure doubles; conversely, expanding the volume to twice its size cuts the absolute pressure in half.
Application: Positive-Displacement Compressors and Compression Ratio
Reciprocating, scroll, rotary, and screw compressors operate on Boyle's Law. A reciprocating compressor draws in a large volume of low-pressure suction gas during the downward piston stroke. On the upward compression stroke, the piston reduces cylinder volume, forcing refrigerant vapor into a tiny clearance volume, raising its pressure until it forces the discharge reed valve open.
The Compression Ratio (CR) measures the degree of mechanical compression:
[!CAUTION] Compression Ratio Exam Trap: Never calculate compression ratio using gauge pressures (psig)! If an R-410A system operates at $118\text{ psig}$ suction and $385\text{ psig}$ discharge, calculating $385 / 118 = 3.26$ is completely wrong. You must add $14.7$ to both values: $\text{CR} = (385 + 14.7) / (118 + 14.7) = 399.7 / 132.7 = \mathbf{3.01:1}$.
2. Charles's Law: Volume-Temperature Relationship (Constant Pressure)
Formulated by Jacques Charles in 1787, Charles's Law states that the volume of a given mass of gas is directly proportional to its absolute temperature, provided the pressure remains constant.
Where $T_1$ and $T_2$ are in degrees Rankine ($^\circ\text{F} + 460$).
Application: Combustion Flue Gas Buoyancy
Charles's Law governs Category I natural draft combustion venting (gas furnaces and water heaters). When fuel gas burns, combustion products heat to 350°F–450°F. According to Charles's Law, heating gas causes it to expand significantly. Because the mass of gas now occupies a larger volume, its density decreases. The surrounding cooler, denser atmospheric air exerts a buoyant upward force, causing flue gases to rise naturally up the chimney flue pipe and vent safely outdoors.
3. Gay-Lussac's Law: Pressure-Temperature Relationship (Constant Volume)
Formulated by Joseph Louis Gay-Lussac in 1802, Gay-Lussac's Law (often termed the Pressure Law) states that the absolute pressure of a given mass of gas is directly proportional to its absolute temperature, provided the volume of the container remains fixed.
Where $P$ is in psia and $T$ is in degrees Rankine ($^\circ\text{F} + 460$).
Application: Nitrogen Pressure Testing & Cylinder Safety
When an HVAC technician pressurizes copper linesets with dry nitrogen to test for leaks, the piping represents a rigid, fixed-volume container ($V_1 = V_2$). If nitrogen is charged to $300\text{ psig}$ during a hot afternoon at 95°F ($555\text{ R}$), and the technician returns the next morning when the temperature has dropped to 55°F ($515\text{ R}$), Gay-Lussac's Law dictates that the pressure must fall:
A pressure drop from $300\text{ psig}$ to $277\text{ psig}$ under these conditions is purely the result of thermal contraction, not a physical piping leak.
4. The Combined Gas Law
Combining Boyle's, Charles's, and Gay-Lussac's Laws yields the Combined Gas Law, which correlates simultaneous variations in pressure, volume, and temperature for a fixed mass of gas:
5. The Ideal Gas Law
The Ideal Gas Law introduces the quantity of gas molecules, expressed in moles ($n$):
Where:
- $P$ = Absolute pressure ($\text{lb}/\text{ft}^2$ or psia)
- $V$ = Volume ($\text{ft}^3$)
- $n$ = Number of moles of gas ($m / M$)
- $R$ = Universal gas constant ($10.73\text{ psia}\cdot\text{ft}^3/[\text{lbmol}\cdot^\circ\text{R}]$) or individual gas constant ($R_{\text{air}} = 53.35\text{ ft}\cdot\text{lb}/[\text{lb}\cdot^\circ\text{R}]$)
- $T$ = Absolute temperature in Rankine ($^\circ\text{R}$)
Dalton's Law of Partial Pressures: Non-Condensable Refrigerant Contamination
Formulated by John Dalton in 1801, Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures that each individual gas would exert if it alone occupied the entire volume at the same temperature:
Atmospheric Partial Pressures
In sea-level atmospheric air at $14.7\text{ psia}$:
- Nitrogen ($78.08%$): $P_{N_2} = 0.7808 \times 14.7 = 11.48\text{ psia}$
- Oxygen ($20.95%$): $P_{O_2} = 0.2095 \times 14.7 = 3.08\text{ psia}$
- Argon & Water Vapor ($0.97%$): $P_{\text{other}} = 0.0097 \times 14.7 = 0.14\text{ psia}$
- Total Pressure: $11.48 + 3.08 + 0.14 = \mathbf{14.70\text{ psia}}$
Dalton's Law in Refrigeration Diagnostics: Non-Condensable Gases
Dalton's Law is the diagnostic key to identifying non-condensable gas contamination in refrigeration circuits. Non-condensables consist of atmospheric air, nitrogen, or carbon dioxide inadvertently introduced due to improper evacuation, leaking suction lines, or contaminated charging hoses.
Inside an operational condenser, refrigerant vapor desuperheats and condenses into liquid at its saturation pressure corresponding to the condensing temperature. However, atmospheric air and nitrogen have critical temperatures well below $-150^\circ\text{F}$ and cannot condense at normal operating temperatures. Consequently, non-condensables collect as trapped gas pockets in the upper coils of the condenser, occupying volume and exerting their own independent partial pressure.
+-----------------------------------------------------------------------------------+
| Symptoms of Non-Condensable Gas Contamination |
+-----------------------------------------------------------------------------------+
| 1. Abnormally High Head Pressure | High discharge gauge reading above PT chart |
| 2. Fluttering High-Side Gauge | Pressure needle vibrates rapidly on manifold |
| 3. High Discharge Temperatures | Compressor runs excessively hot; oil breakdown|
| 4. Increased Amp Draw | Compressor motor overworks against high head |
| 5. Loss of System Cooling | Reduced evaporator feed; high power bills |
+-----------------------------------------------------------------------------------+
Diagnostic Field Test for Non-Condensable Gases
- Disconnect compressor electrical power to stop operation.
- Force the outdoor condenser fan to run continuously (or let the system stand idle overnight in a shaded space) until the entire condenser coil temperature equalizes with the outdoor ambient dry-bulb temperature.
- Measure outdoor ambient dry-bulb temperature accurately using a calibrated digital thermometer placed at the condenser inlet.
- Connect a precision pressure gauge to the high-side service port and measure static system pressure.
- Look up the expected saturation pressure on a Refrigerant Pressure-Temperature (PT) chart corresponding to the measured ambient temperature.
- Evaluation: If the measured gauge pressure is higher than the PT chart saturation pressure (by more than $3\text{ to } 5\text{ psi}$), non-condensables are present in the system. The system must be recovered, evacuated below 500 microns, and recharged with virgin refrigerant.
Avogadro's Law and Fuel Gas Combustion Calculations
Avogadro's Law states that equal volumes of all ideal gases at identical temperature and pressure contain an equal number of molecules ($V \propto n$).
In HVAC fuel gas systems (governed by the International Fuel Gas Code - IFGC), Avogadro's Law establishes the volumetric air requirements for complete combustion:
- Natural Gas (Methane - $\text{CH}_4$): One cubic foot of methane requires 2 cubic feet of pure oxygen. Because atmospheric air contains only 20.95% oxygen, supplying 2 cu ft of oxygen requires $2 / 0.2095 = \mathbf{9.55\text{ cu ft of air}}$ (nominally $10\text{ cu ft of air per cu ft of natural gas}$).
- Liquefied Petroleum Gas (Propane - $\text{C}_3\text{H}_8$): One cubic foot of propane requires 5 cubic feet of pure oxygen, requiring $5 / 0.2095 = \mathbf{23.87\text{ cu ft of air}}$ (nominally $24\text{ to } 25\text{ cu ft of air per cu ft of propane}$).
If air supply is restricted below these stoichiometric volume ratios, incomplete combustion occurs, producing deadly carbon monoxide (CO), aldehydes, and soot.
Step-by-Step Worked Engineering Calculations
Calculation 1: Compression Ratio of an R-410A Heat Pump
Problem: An R-410A split-system heat pump operates with a suction pressure of $125\text{ psig}$ and a liquid discharge head pressure of $395\text{ psig}$. Assuming standard atmospheric pressure of $14.7\text{ psia}$, calculate the absolute compression ratio of the compressor.
Step 1: Convert suction pressure from gauge to absolute (psia)
Step 2: Convert discharge pressure from gauge to absolute (psia)
Step 3: Calculate compression ratio (CR)
Result: The operating compression ratio is 2.93:1.
Calculation 2: Nitrogen Holding Pressure Temperature Compensation
Problem: A newly installed VRF copper piping network is pressurized with dry nitrogen to $400\text{ psig}$ at an afternoon temperature of 90°F. The following morning, the line temperature has dropped to 60°F. The pressure gauge now reads $373\text{ psig}$. Determine if the system is leaking or if the pressure change is entirely thermal.
Step 1: Convert initial and final temperatures to absolute Rankine
Step 2: Convert initial pressure to absolute psia
Step 3: Apply Gay-Lussac's Law to calculate expected pressure ($P_2$)
Step 4: Convert expected absolute pressure back to gauge pressure (psig)
Diagnostic Conclusion: The expected gauge pressure due purely to thermal contraction is $377.4\text{ psig}$. Because the actual measured pressure is $373\text{ psig}$ ($4.4\text{ psi}$ lower than expected), a minor physical piping leak is present.
Calculation 3: Trapped Non-Condensable Partial Pressure
Problem: An idle R-134a refrigeration system stands in a 70°F mechanical room overnight. The technician connects a gauge manifold and measures a static pressure of $85.0\text{ psig}$. According to an R-134a PT chart, pure saturated R-134a at 70°F exhibits a vapor pressure of $71.1\text{ psig}$. What is the partial pressure exerted by non-condensable gases in this system?
P_{\text{non-condensables}} &= P_{\text{measured}} - P_{\text{saturation (PT chart)}} \\ &= 85.0\text{ psig} - 71.1\text{ psig} = \mathbf{13.9\text{ psi}} \end{aligned}$$ *Result*: Trapped non-condensable air is exerting **13.9 psi** of excess partial pressure inside the refrigeration circuit. --- ## Master Summary Table of Governing Gas Laws | Gas Law Name | Mathematical Equation | Held Constant | Primary HVAC Application | | :--- | :--- | :--- | :--- | | **Boyle's Law** | $P_1 V_1 = P_2 V_2$ | Temperature ($T$) | Compressor cylinder compression; compression ratio | | **Charles's Law** | $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ | Pressure ($P$) | Combustion flue gas buoyancy; chimney natural draft | | **Gay-Lussac's Law** | $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ | Volume ($V$) | Nitrogen pressure testing; recovery cylinder heating | | **Combined Gas Law** | $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ | Gas mass ($m$) | Combined multi-variable gas expansion and compression | | **Ideal Gas Law** | $P V = n R T$ | Universal ($R$) | Exact thermodynamic modeling of superheated gases | | **Dalton's Law** | $P_t = P_1 + P_2 + \dots + P_n$ | Temperature, Volume | Non-condensable air contamination in condenser coils | | **Avogadro's Law** | $V \propto n$ | Pressure, Temperature | Combustion air stoichiometry for natural gas and LP |An air-conditioning compressor operates with a suction pressure of 118 psig and a discharge pressure of 395 psig. Assuming standard sea-level atmospheric pressure of 14.7 psia, what is the compression ratio of this operating compressor?
A technician charges a rigid piping network with dry nitrogen to 300 psig at 95°F. Over the weekend, the ambient temperature drops to 50°F. If no nitrogen has leaked, what gauge pressure should the technician expect to read on the manifold gauge?
According to Dalton's Law of Partial Pressures, what is the operational consequence of having trapped non-condensable atmospheric air inside a refrigeration system condenser coil?
Under the International Fuel Gas Code and Avogadro's combustion stoichiometry, approximately how many cubic feet of atmospheric air are required to achieve complete combustion of exactly 1 cubic foot of natural gas (methane)?