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Explain why kilowatt hour is a unit of energy not power.
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Explain why kilowatt hour is a unit of energy not power.
A kilowatt hour () is a unit of energy because it represents the product of power (kilowatt) and time (hour). Energy is defined as the capacity to do work, and it is calculated by multiplying the rate at which work is done (power) by the duration over which it is done (time). Power, on the other hand, is the rate of energy transfer or consumption, measured in watts or kilowatts.
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In the following questions, use a tariff of per kilowatt hour (including VAT).
Part a· 4 steps
Four energy saving bulbs are switched on for in the evening. Calculate cost ().
Calculate the total power of the bulbs.
$$ \text{Total Power} = 4\, \text{bulbs} \times 15\, \text{W/bulb} = 60\, \text{W} $$Convert the total power from watts to kilowatts.
$$ \text{Total Power} = 60\, \text{W} \times \frac{1\, \text{kW}}{1000\, \text{W}} = 0.060\, \text{kW} $$Calculate the total energy consumed in kilowatt hours.
$$ \text{Energy} = \text{Power} \times \text{Time} $$ $$ \text{Energy} = 0.060\, \text{kW} \times 5\, \text{hours} = 0.30\, \text{kWh} $$Calculate the total cost.
$$ \text{Cost} = \text{Energy} \times \text{Tariff} $$ $$ \text{Cost} = 0.30\, \text{kWh} \times \text{R1.50/kWh} = \text{R}0.45 $$ The cost is $\boxed{\text{R0.45}}$.
Part b
Calculate the cost of using a heater for and .
Convert the power from watts to kilowatts.
$$ \text{Power} = 100\, \text{W} \times \frac{1\, \text{kW}}{1000\, \text{W}} = 0.100\, \text{kW} $$Convert the total time to hours.
$$ \text{Time} = 3\, \text{hours} + 30\, \text{min} \times \frac{1\, \text{hour}}{60\, \text{min}} $$ $$ \text{Time} = 3\, \text{hours} + 0.5\, \text{hours} = 3.5\, \text{hours} $$Calculate the total energy consumed in kilowatt hours.
$$ \text{Energy} = \text{Power} \times \text{Time} $$ $$ \text{Energy} = 0.100\, \text{kW} \times 3.5\, \text{hours} = 0.35\, \text{kWh} $$Calculate the total cost.
$$ \text{Cost} = \text{Energy} \times \text{Tariff} $$ $$ \text{Cost} = 0.35\, \text{kWh} \times \text{R1.50/kWh} = \text{R}0.525 $$ The cost is $\boxed{\text{R0.53}}$.
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