Unit Systems

Much of the heating industry uses traditional units, the British Thermal Unit (Btu), hours (hr or h), Fahrenheit (F), pounds mass (lbm), feet (ft) and inches (in), then confuses things by mixing in kilowatts (kW) and kilowatt-hours (kWh) for electrical supplies. You can do detailed design calculations in these traditional units, but it gets messy and you are likely to make mistakes. You will be much better off using consistent SI units of Joules (J), seconds (s), Watts (W), Celsius (C) or Kelvin (K), kilograms (kg), and metres (m) in your calculations and only converting to other units when you need to make comparisons to the product literature. Also avoid doing calculations with kW, kJ, cm, etc. to avoid introducing errors of 100 or 1000 into your results!

Energy, Power and Time

Managing energy in a building requires you to keep track of stored energy and how that energy changes over time depending on the power and heat flows into and out of the building.

Energy

The SI unit of energy is the Joule (J). Mechanically 1 J = 1 Nm, the energy associated with lifting a 1 Newton (N) weight up by 1 metre (m) in a gravity field. So the potential energy is $mgh$.

Lifting a 0.6 kg cup of coffee (about half coffee, and half cup) by 1/2 m to my mouth requires useful energy expenditure of about 3 Joules.

The thermal energy needed to warm a substance is defined as its specific heat capacity. Water has a specific heat $C_p = 4180\units{J/kgK}$ meaning it takes 4180 Joules to increase the temperature of 1 kilogram of water by 1 degree Kelvin (or Celsius). Air has a specific heat at constant pressure of $1004\units{J/kgK}$ and most building materials are in the range $500 – 1500 \units{J/kgK}$ so it’s not a bad guess the coffee cup has a specific heat around 1000.

Warming the coffee (water) and the cup from room temperature up to 60 C will require about 60,000 J.

Chemical energy released when you burn a fuel is is defined as specific heat of combustion. Ethanol is lighter than water and has a specific heat of combustion of $30\units{ MJ/kg}$ meaning that burning a kilogram of ethanol will release about 30,000,000$\;$ J of heat.

Burning a coffee cup full of ethanol would produce heat release of about 7,000,000 J.

Chemical energy is orders of magnitude larger than thermal energy, which is orders of magnitude larger than mechanical energy in most practical situations. Very often we use kiloJoules (kJ), megaJoules (MJ), or gigaJoules (GJ) to cope with the scale in reasonable numbers.

Properties vary with conditions, but not enough to worry about for the estimates we will make in this design.

Other Energy Units

1 Watt hour = 3600 J because 1 W is a Joule/second and there are 3600 seconds in an hour.

Traditional, non SI, units can have slightly different definitions depending on the application, so conversions are approximate.

1 British thermal unit (BTU or Btu) is about 1060 J.

1 calorie (cal) is about 4.2 J, unless you are talking about food when calories are actually kilocalories (kcal) and 1 kilocalorie is about 4200 J. Thus a human who eats a 2000 calorie diet can be expected to give off about 8400000 J/day or about 100 J/s, most of it as heat.

Power

The SI unit of power is the Watt (W), often also kiloWatt (kW), megaWatt (MW), or gigaWatt (GW) to cope with orders of magnitude. 1 W is 1 J/s, energy delivered or expended per unit time.

Mechanical, thermal, and chemical equivalents to energy are all just about how quickly that energy moves from one place to another.

Electrical power is the result of current motion in a circuit, a given current at a given voltage. 1 W is also the power delivered by 1 Ampere of current flowing at a potential of 1 Volt. Thus electrical power is

\begin{equation}

P = VI

\end{equation}

for both DC and AC circuits because of the way we define voltage and current for the constantly varying levels of alternating current. An Arduino drawing 50 milliamps (mA) at 5 volts from a USB port is using 0.25 W, while a kettle drawing 10 A at 115 VAC is using 1150 W, enough that it could be significant to a building energy balance.

Electrical energy is usually quantified in units of Power x Time, like kiloWatt hours (kWh or kWhr). Energy stored in a battery is usually quantified as Current x Time, with the battery voltage implied. A 100 Amp hour (Ah or Ahr) automotive battery weighing about 30 kg, could supply 5 Amps for 20 hours at about 12 VDC. That would be 5 x 12 = 60 W over that time or a total of 60 x 20 x 3600 s/h = 4320000 J over those 20 hours, about 1/2 the energy content of that coffee cup of ethanol.

Other Power Units

1 Btu/h = 0.293 W is commonly used for heating and cooling systems. Product advertising often says simply 12000 BTU leaving off the “per hour”. 1 W = 3.412 Btu/hr.

1 ton of air conditioning or refrigeration is enough to freeze a ton of water over a day = 12000 Btu/h = 3517 W.