Basic Mathematics, Thermodynamics, and Applied Science
What this domain tests
Basic Mathematics, Thermodynamics, and Applied Science supplies the arithmetic and physical principles behind every other domain: heat quantities, sensible and latent heat, pressure and head, power conversion, and the three modes of heat transfer.
Core rules
- One Btu raises one pound of water by one degree Fahrenheit. Specific heat of water is 1.0 Btu/lb-deg F.
- Latent heat of vaporisation at atmospheric pressure is about 970 Btu/lb; superheat is heat added to steam above saturation temperature.
- One boiler horsepower equals 33,475 Btu/h, roughly 34.5 lb of steam per hour from and at 212 deg F.
- Pressure and head: one psi equals 2.31 ft of water, or one foot of water equals 0.433 psi. Atmospheric pressure is about 14.7 psia.
- Heat transfer modes: conduction through metal, convection to the water or gas, radiation in the furnace. Heat always flows from hot to cold.
- Useful formulas: Q = m x c x delta T for sensible heat; Q = m x latent heat for evaporation; efficiency = output / input.
Worked example
How much heat is needed to take 500 lb of water at 60 deg F to saturated steam at 212 deg F? Sensible heat = 500 x 1.0 x (212 - 60) = 500 x 152 = 76,000 Btu. Latent heat = 500 x 970 = 485,000 Btu. Total = 76,000 + 485,000 = 561,000 Btu. At a firing rate of 33,475 Btu/h, that is about 16.8 boiler horsepower-hours, which is why evaporation rates are always quoted with the firing rate attached.
Traps that cost marks
- Mixing gauge pressure with absolute pressure; absolute equals gauge plus 14.7.
- Forgetting the latent heat, which is far larger than the sensible heat in most problems.
- Using degrees Celsius in Btu formulas without converting.
- Confusing psi with feet of head.