A previous mathematical derivation was used to determine that an electron volt ( eV ) is a quantity of energy carried by an electron that accelerates through an electric field. We will now see that the kilowatt-hour ( kWh ) is also a unit of energy; it is a quantum of energy carried by a coulomb ( C ) of charge that traverses an electric circuit. Please recall that a watt ( W ) describes the rate at which joules ( J ) of energy are liberated or consumed within an electrical system:
W = ( J / s )
1 kW = 1,000 J / s
In order to determine how much energy 1 kWh contains, we must determine how many seconds transpire within an hour:
( 1 hr )( 60 min / 1 hr )( 60 s / 1 min ) = 3,600s
We now have what is needed to determine how much energy a 1 kW source of power dissipates within an hour:
( 1 kW )( 1 hr ) = 1 kWh
( 1 kWh )( 3,600 s / 1 hr ) = 3,600 kJ
Nonetheless, a price-per-kWh rating established by a power company eliminates the need for customers to know the exact number of joules liberated or consumed per hour:
Q: A water heater has a power rating of 2,500 W. How much does it cost to run the heater for one day at a rate of $0.11 per kWh?
A: ( 2,500 W ) = 2.5 kW
( 2.5 kW )( 24 hr ) = 60 kWh
( 60 kWh )( $0.11 / 1 kWh ) = $6.6 dollars
Q: During a 24 hour period of time, the following appliances consumer power over varying lengths of time:
air conditioner: 15 hr
blow dryer: 10 min
clock: 24 hr
clothes dryer: 1 hr
dishwasher: 45 min
microwave oven: 15 min
refrigerator 12 hr
television: 2 hr
water heater: 8 hr
At a rate of $0.11 per kWh, what is the electric bill on this day?
A: We must first determine the total quantity of kWh consumed. In order to do so, we must know the power rating of each appliance. We then multiply the power rating of each appliance by the amount of time it was running:
air conditioner: 860 W
blow dryer: 1,000 W
clock: 2 W
clothes dryer: 4,000 W
dishwasher: 1,200 W
microwave oven: 800 W
refrigerator: 500 W
television: 250 W
water heater: 2,500 W
*** Three significant digits are acceptable in final calculations due to the tolerance settings of most electrical measuring devices. Follow other specifications as indicated. ***
air conditioner: ( 0.86 kW )( 15 hr ) = 12.9 kWh
blow dryer: ( 1.0 kW )( 0.167 hr ) = 0.167 kWh
clock: ( 0.002 kW )( 24 hr ) = 0.048 kWh
clothes dryer: ( 4.0 kW )( 1 hr ) = 4.0 kWh
dishwasher: ( 1.2 kW )( 0.75 hr ) = 0.9 kWh
microwave oven: ( 0.8 kW )( 0.25 hr ) = 0.2 kWh
refrigerator: ( 0.5 kW )( 12 hr ) = 6 kWh
television: ( 0.25 kW )( 2 hr ) = 0.5 kWh
water heater: ( 2.5 kW )( 8 hr ) = 20 kWh
Thus, the total quantity of energy consumed is as follows:
( 12.9 + 0.167 + 0.048 + 4.0 + 0.9 + 0.2 + 6 + 0.5 + 20 )( kWh ) = 44.715 ≅ 44.7 kWh
The electric bill for the day may now be tabulated:
( 44.7 kWh )( $0.11 / 1kWh ) = $4.92
RENAISSANCE PHYSICS 