Physics of Buildings

Sources and simplifications

Every reference cited on this site, and every place a figure idealizes the real system.

References

  1. U.S. Geological Survey. Water Density (Water Science School). USGS. government reference Density table: 0.99907 g/cm³ at 60 °F (15.6 °C), 0.98870 at 120 °F (48.9 °C), 0.98338 at 140 °F (60 °C). (How the tank works)
  2. McClellan, W. T. (2011). High-efficiency water heater dip tube and method for reducing turbulence in water heaters, US 7,861,678 B2 (granted 2011). U.S. Patent and Trademark Office. patent The dip tube brings cold inflowing water down to the bottom of the heating chamber; preserving natural stratification is highly desirable; mixing of heated and incoming water impairs the heater's useful output. (How the tank works)
  3. A. O. Smith Corporation (2021). Installation Instructions and Use & Care Guide: Residential Gas Water Heaters, 100341468_2000598643 Rev A (March 2021). A. O. Smith, sold through Lowe's (AOSmithAtLowes.com). manufacturer manual Component diagram (anode, inlet dip tube, T&P valve); every heater has at least one anode rod; rotten-egg odor needs sulfate, little oxygen, sulfate-reducing bacteria and active hydrogen from the anode; less active anode plus chlorination by a service agency; do not remove the anode; condensation sizzling and popping in the burner area is normal; expansion noises are normal; T&P valve must not be plugged; most T&P leakage is thermal expansion in a closed system; thermostatic mixing valves; short repeated heating cycles can raise temperature up to 30 °F above the setting; drain and flush every 6 months. (How the tank works)
  4. Abu Hilal, M. (2011). Experimental Energy Study for Domestic Hot Water Storage Tanks. Jordan Journal of Mechanical and Industrial Engineering (abstract via An-Najah National University). journal article Turbulent mixing at the cold inlet must be eliminated to save energy in the tank; a curved cover on the bottom supply line gave about 17% more usable hot water. (How the tank works)
  5. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §5.1 Energy Basics (Table 5.1, specific heats). OpenStax, Rice University. textbook Specific heat of liquid water 4.184 J/(g·°C) at 25 °C. (How the tank works)
  6. Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI), NIST SP 811, Appendix B.8 Factors for units listed alphabetically. National Institute of Standards and Technology. standard Btu_IT = 1055.056 J; Btu_IT/h = 0.2930711 W; US gallon = 3.785412 × 10⁻³ m³; lb = 0.4535924 kg; °F interval = 5/9 K. (How the tank works)
  7. U.S. Department of Energy. 10 CFR Part 430, Subpart B, Appendix E: Uniform Test Method for Measuring the Energy Consumption of Water Heaters. Electronic Code of Federal Regulations (eCFR), current as of 2026. federal regulation §1.5 first-hour rating: estimate of the maximum volume of hot water a storage heater can supply within an hour that begins fully heated; §2.3 supply water 58 °F; §2.4 outlet 125 °F; §5.3.3 draws at 3.0 gpm (tanks ≥ 20 gal), each ended when the outlet falls 15 °F below its maximum; electric heaters with two or more elements that do not operate simultaneously; §1.11 recovery efficiency. (How the tank works)
  8. A. O. Smith Corporation. ProLine 40-Gallon Atmospheric Vent Short Natural Gas Water Heater, model GCBL-40 400 (product page). hotwater.com. manufacturer data sheet 40-gallon nominal (38 gal rated storage), 40,000 Btu/h input, 68-gallon first-hour rating, recovery 41 gallons per hour, UEF 0.57. (How the tank works)
  9. A. O. Smith Corporation (2021). Installation Instructions and Use & Care Guide: Residential Electronic Thermostat Electric Water Heater (printed 10/21/2021). A. O. Smith, sold through Lowe's (AOSmithAtLowes.com). manufacturer manual Upper and lower element; the control energizes one element at a time and the upper has priority; limp mode with one failed element; troubleshooting 'insufficient hot water': undersized heater, temperature set low, faulty thermostatic mixing valve in a shower control, reversed connections or melted dip tube (soon after installation), leak, failed lower element ('some hot water but not as much as before'; the lower element does most of the work and usually wears out first); 4500/5500 W elements; inspect the anode after six months, then at least annually depending on hardness. (How the tank works)
  10. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §17.6 Corrosion. OpenStax, Rice University. textbook Rusting of iron as a galvanic cell; cathodic protection: connecting iron to a more active metal such as zinc or magnesium; 'also used to protect the metal parts in water heaters'; sacrificial anodes are used up and must be monitored and replaced. (How the tank works)
  11. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, Appendix L: Standard Electrode (Half-Cell) Potentials. OpenStax, Rice University. textbook E° (V): Mg²⁺/Mg −2.372; Al³⁺/Al −1.662; Zn²⁺/Zn −0.7618; Fe²⁺/Fe −0.447. (How the tank works)
  12. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §17.7 Electrolysis (Faraday's constant, Q = nF). OpenStax, Rice University. textbook Charge transferred for n moles of electrons is Q = nF; current × time gives the charge and hence the moles of metal. (How the tank works)
  13. NIST Physical Measurement Laboratory. CODATA Value: Faraday constant. National Institute of Standards and Technology. standard F = 96 485.332 12 C/mol (exact). (How the tank works)
  14. IUPAC Commission on Isotopic Abundances and Atomic Weights. Standard Atomic Weights (2024). CIAAW. standard Mg [24.304, 24.307] (24.305 used); Al 26.981 5384; Zn 65.38; Fe 55.845. (How the tank works)
  15. Veilleux, V. (Corro-Protec) (2023). Decoding the Science: The Functioning of Powered Anode Rods (1 May 2023). Corro-Protec (manufacturer of powered anodes). manufacturer article Powered (impressed-current) anodes: a titanium or similarly inert rod connected to an external power supply that drives a direct current from the rod to the tank; the rod is not consumed. (How the tank works)
  16. Leonard, J. and Content Creation Team. Corrosion Protection (Hot Water University guide). Hot Water University (hotwateruniversity.dozuki.com). trade training guide Anode rods are typically made from magnesium, aluminum or zinc alloys; have a plumber check the anode after the first six months, then annually; water softeners reduce anode life. (How the tank works)
  17. U.S. Consumer Product Safety Commission. Avoiding Tap Water Scalds (CPSC Document #5098). U.S. Consumer Product Safety Commission, Bethesda, MD. government safety alert Urges all users to lower water heaters to 120 °F; most adults suffer third-degree burns from 150 °F water in 2 s, 140 °F in 6 s, 130 °F in 30 s, and even 120 °F in 5 min; most injuries are to the elderly and children under five; measure at the tap with a thermometer. (How the tank works)
  18. Friedman, D. (InspectAPedia). Hot Water Heater Noise Diagnosis. InspectAPedia. reference website Scale forms as minerals precipitate at the hottest points, often the tank bottom; thicker scale means worse banging and popping; scale on the bottom insulates it, raising its temperature and weakening the tank bottom; crackling on electric heaters can be scale on the elements. (Popping, Rumbling, Running Out)
  19. U.S. Occupational Safety and Health Administration. Legionnaires' Disease: Control and Prevention. OSHA. government reference Water heaters maintained below 140 °F that contain scale and sediment may foster Legionella growth; storing domestic hot water at a minimum of 140 °F and delivering at a minimum of 122 °F to outlets; high temperatures carry a serious burn risk. (Popping, Rumbling, Running Out)
  20. ENERGY STAR (U.S. EPA and DOE). Heat Pump Water Heaters: How It Works. ENERGY STAR. government reference Uses electricity to move heat rather than make it, like a refrigerator in reverse, drawing heat from the surrounding air into the tank; operating modes; during high demand switches automatically to standard electric resistance heating ('hybrid'). (Popping, Rumbling, Running Out)
  21. U.S. Environmental Protection Agency. WaterSense: Showerheads. EPA. government reference Standard showerheads use 2.5 gpm; WaterSense-labeled showerheads use no more than 2.0 gpm; less shower water reduces demand on water heaters. (Shower-time calculator)

Simplifications