Back to main pageEnergy and Power: units and definitions
I feel obliged to talk about something of everyday importance. Nothing is more important than money,they say, and it takes money to pay our hydro and gas bill.
Power and Energy
Energy has a precise definition in physics and engineering even though it is used loosely in every day life. Likewise power is defined precisely in spite of its everyday usage which seems almost the same as energy. In fact power is defined as the rate work is done or, saying it another way, the rate of energy transfer or of energy usage.P = ΔE/Δt
Thus the units of power in the SI system are joules/second. Power is so common that its unit is called the watt. Thus
1 W = 1 J/s.
Electricity is usually measured in kW-h (kilowatt-hours). Because there are 3600 s in one hour 1 kW-h = 3600 kJ = 3.6 MJ.
The price of electricity in BC now is $0.06/kW-h. This is extremely cheap by world standards (see The Economist, March 1, 1997, p66 or refer to BC Hydro's web site.). In Japan it costs nearly 3 times as much. Still this is expensive compared to our price of natural gas.
Natural gas is now billed in gigajoules. The cost of natural gas per gigajoule varies, but as of 2009 the cost of $6/GJ is typical. (The gas conversion factor on your gas bill, apx 0.11, converts the gas meter reading, which is in 1000 cubic feet of gas, to GJ. Thus 1 GJ is about 9000 cubic feet of gas or about the volume of a big lecture hall.)
Converting the price of electricity to $/GJ we find
($0.06/3600MJ) x (1000 MJ/GJ) = $17/GJ
The only catch, at least for heating, is that the efficiency of converting energy to heat energy is greater for electricity than for gas. Electricity can be converted at 100% efficiency whereas gas, in modern furnaces or boilers, is usually converted at 70% to 80% efficiency.
Food Energy
In bygone days heat energy was traditionally measured in another unit: the calorie. The calorie is defined as the energy needed to raise one gram of water 1° C. Careful experiments show that mechanical energy can heat water, or anything else. By churning water in a well-insulated container it was found that one calorie of heat energy is equivalent to 4.19 J:1 calorie = 4.19 J
Because all energy is equivalent, there is no reason to measure heat in different units than other forms of energy, and now you will notice that food energy is usually quoted in joules as well as calories. However for the purpose of nutrition the calorie is inconveniently small. Therefore the food Calorie used in nutrition (spelled with a big C) is really a kilocalorie:
1 Calorie = 1000 calories =4.19 kJ
How much does one GJ of energy cost from food. Sugar and other carbohydrates usually have about 17 kJ (4 Cal) per gram. Sugar costs about $0.12/100 g.
($.12/100g) x ( 1 g/17 kJ) x (1000000 kJ/GJ) = $70/GJ.
BTUs and Horsepower
If you ever buy a furnace or hot-water heater in this country, you will find that they are rated in BTU/h. (Sometimes they just say BTU when they mean BTU/h.) BTU stands for British Thermal Unit which is the energy it takes to heat one pound of water one degree Fahrenheit. Thus1 BTU = 454 g x (5/9) °C = 252.22 cal = 1057 J.
For practical purposes one can approximate 1BTU = 1 kJ.
A typical furnace is rated at 100,000 BTU/h.
(100,000 BTU/h) x ( 1h/3600 s) x (1.057 kJ/BTU) = 29,000 J/s = 29 kW
A typical electrical heater uses 1 kW (converting it to heat at 100% efficiency). If one allows for the furnace efficiency of 75% then a 100,000 BTU/h furnace is equivalent to about 22 one-kW electrical heaters.
A horsepower is a measure of power developed by the ancient British and we still find it around sometimes.
It's about 750 watts or 3/4 kW.1 hp = 745.7 watts.
Question: How many horsepower is a typical furnace?
(For the purposes of passing this course's exam, just remember the definition of power and what a watt is. You may need some of the other stuff in real life so just remember where to look it up.)Nuf said.