BTU per pound-Fahrenheit
Specific heat capacityexact by definition
The BTU per pound per Fahrenheit degree is the customary US unit of specific heat, and it is exactly 4186.8 J/(kg·K) when the International Table BTU is used, as it is here. The factor follows exactly from the IT BTU of 1055.05585262 J, the pound of 0.45359237 kg and the Fahrenheit degree of 5/9 kelvin, so it is exact by definition rather than measured. Liquid water is 1.00 BTU/(lb·°F) by construction, which is the number behind almost every HVAC rule of thumb.
Watch out: The Fahrenheit in the denominator is an interval, not a reading. A specific heat of 1 BTU/(lb·°F) means one BTU per pound for each Fahrenheit degree of RISE, so heating 100 lb of water by 20 F° takes 2000 BTU. No offset enters anywhere.
| 1 BTU/(lb·°F) | 4,186.8 J/(kg·K) |
One BTU/(lb·°F) equals one kcal(IT)/(kg·°C) exactly, a coincidence that is not a coincidence: both units were defined by the heating of water, and the pound-to-Fahrenheit ratio happens to mirror the kilogram-to-Celsius one.
About the btu per pound-fahrenheit
This unit is the hidden constant inside the two most-used equations in North American HVAC. Water's specific heat is 1 BTU/(lb·°F) and its density is about 8.33 lb/gal, so heat carried by a water loop is \(Q = 8.33 \times 60 \times \text{gpm} \times \Delta T = 500 \times \text{gpm} \times \Delta T\) BTU/h. That familiar 500 is nothing but pounds per hour per gpm times a specific heat of one. On the air side, standard air weighs about 0.075 lb/ft³ and has a specific heat near 0.24 BTU/(lb·°F), giving \(0.075 \times 60 \times 0.24 = 1.08\), the constant in \(Q = 1.08 \times \text{cfm} \times \Delta T\).
Both constants quietly assume standard conditions. The 500 drifts if the loop carries glycol, which has a lower specific heat and a higher density: a 30 percent propylene glycol mix runs closer to 475, and a 50 percent mix closer to 450, so a system designed on 500 and filled with glycol will move less heat than the drawings promise. The 1.08 drifts with altitude, because air density falls: in Denver it is closer to 0.89. Neither correction is difficult, and both are skipped often enough to be worth naming.