Topic 2 of 4
Energy use and cost
An electricity charge depends on energy used. Work out the power and operating time in matching units before applying the price per unit of energy.
Power is energy transferred per second. At constant power, E = Pt; use the interval's average power if it varies. A larger power means a faster energy transfer, but the total also depends on time.
A kilowatt-hour is an energy unit
One kilowatt-hour, written kW h or kWh, is the energy transferred by a power of 1 kW maintained for 1 hour.
A kilowatt is a unit of power; a kilowatt-hour is a unit of energy. The hour multiplies the power. Writing kW/h would mean a rate of change of power and does not describe the energy used here.
Use hours with kilowatts
The same heater, with a supplied tariff
The heater uses 1.15 kW for 12 minutes. First, t = 12/60 = 0.20 h.
Energy = 1.15 x 0.20 = 0.230 kW h. This is also 0.230 x 3 600 000 = 828 000 J.
Use an example tariff of $0.30 per kW h. Cost = 0.230 x $0.30 = $0.069, or 6.9 cents.
If the answer is required to the nearest cent, this is $0.07. Keep the unrounded energy and cost until the final step. The tariff here is a supplied example price.
Compare the complete use pattern
Appliance A
0.10 kW for 5.0 h
Energy = 0.10 x 5.0 = 0.50 kW h.
Appliance B
1.0 kW for 0.25 h
Energy = 1.0 x 0.25 = 0.25 kW h.
B has ten times the power but runs for much less time. It uses half as much energy as A in these stated patterns. At the same tariff, its energy cost is also half as much.
A thermostat can turn a heater on and off. If a 1 kW heater is powered for only part of an hour, its energy use is not automatically 1 kW h. Use its total powered-on time at that power, or a supplied average power over the whole interval. Include any other energy use if the question specifies it.
Check the time unit. Twelve minutes is 720 s or 0.20 h. It is neither 12 h nor 0.12 h. Choose seconds for a calculation in joules and hours for a calculation using kilowatts and kilowatt-hours.