Power

Power

• Definition: The amount of energy converted to heat, light, sound or motion per unit of time

• Unit: Power is measured in watts (W)• Naming: Named after James Watt, a Scottish

inventor and engineer

Some MathRemember: Power is the amount of energy

converted to heat, light, sound or motion every second.

Quantity Symbol

Power P

Energy E

Time t

Et

P =

E

P t

P

I V

P = I x V

% Efficiency

• It is possible to calculate how efficient an electrical device is (such as a kettle at heating up water)

• No device is 100% efficient

Percent efficiency =Useful energy output

Total electrical energy inputx 100%

Efficiency of a kettle problemAn electric kettle has a power rating of 1000W. It takes the kettle 4.0 minutes to heat 600mL of water from 22oC to 100oC. If it takes 1.96x105J of energy to heat the water, what is the efficiency of the kettle?

G: P = 1000 W t= 4.0 minutes (240s) useful energy output = 1.96 x 105 J (196 000 J)R: Percent efficiencyA:

S:S:

Percent efficiency =Useful energy output

Total electrical energy input x 100 %

E

tP =

Chemists have shown that it takes 4180J of energy to raise the temperature of

1kg of water by 1oC

Chemists have shown that it takes 4180J of energy to raise the temperature of

1kg of water by 1oC

Calculating the Cost of Energy Use

• Step 1 – Find the device’s power rating in “W” (watts) , time of use (s, min, h, etc) and

price charged (¢ per kW·h)• Step 2 – Convert to “kilowatts” (kW)and

“hours” (h)• Step 3 – Calculate the Energy used by the

device using E = P x t, units “kW·h”• Step 4 – Calculate the total cost = E x price

Household Audit Sample Problem You run your 1200 W dishwasher every night before you go to sleep for 30 min each time. Calculate the total weekly cost if your off-peak price is 7.0¢ per kW·h.

P = 1200W t = 30 min Price = 7.0¢ per kW·h 1000 W = 1kW 60 min = 1h 1 wk = 7 dP = 1.2 kW t = 3.5 h (0.5 h x 7 d) E = P x t Total cost = E x Price = 1.2 kW x 3.5 h = 4.7 kW·h x 7.0¢/kW·h = 4.7 kW·h = 32.9 ¢It will cost about 33¢ to run the dishwasher this week.