This problem is good practice for how to seem sciency to your friends after grad

Question

This problem is good practice for how to seem sciency to your friends after graduating. Your power bill comes in units of kWh, or kilowatt astir hours. What do these units measure (power, potential, energy, current, something else)? (Dimensional analysis may be useful.) Convert 1 kWh to a more familiar unit (kg, m, s, J, V, C, A, W, etc, or a basic combination of those). A space heater has an average power usage of 1500 W when plugged into a 120 V outlet. Determine how much energy the space heater uses if you run it for 4 hours each day. Feel free to use whatever units are most convenient. A typical energy rate is dollar0.11/kWh. How much does your space heater cost to run each day?

Explanation / Answer

Kilowatt-hour = 1000 watt x hour = 1000 (J/s) x 60x60 s [ unit of watt is J/s]

= 3.6 x 106 J

Clearly we can see that 1 kilowatt-hour is equivalent to 3.6 x 106 J, So kilowatt-hour represents energy (Here electrical energy)

1kilowatt-hour = 3.6 x 106 J or

= 3.6 x 106 (kg-m2)/s2

b) Energy used by space heater each day = 1500 x 4 x 60 x 60 J (E = P x t)

= 21600000 J

= 6 kWh

c) Cost to run space heater each day = 0.11 x 6

= $0.66

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