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Power and energy are often used interchangeably but they are quite different Energy is measured...

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Calculus

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Power and energy are often used interchangeably but they are quite different Energy is measured in units of joules J or Calories Cal where 1 Cal 4184 J On the other hand power is the rate at which energy is used and is measured in watts W 1 W 1 J s Other useful units of power are kilowatts kW and megawatts 1 MW 106 W If energy is used at a rate of 1 kW for 1 hr the total amount of energy used is 1 kilowatt hour kWh which is 3 6x 106 J Suppose the power function of a large city over a 24 hr period is given by P t E t 255 170 sin t 12 where P is measured in MW and t 0 corresponds to 6 00 p m see accompanying figure Complete parts a through d below Click the icon to view the graph of P t E t 255 170 sin t 12 C a How much energy is consumed by this city in a typical 24 hr period Express the answer in MWh and in J The energy consumed in a typical 24 hour period in MWh is 6120 MWh Simplify your answer 13 The energy consumed in a typical 24 hour period in J is 2 2032 10 J Simplify your answer Use scientific notation b Burning 1 kg of coal produces about 450 kWh of energy How many kg of coal are required to meet the energy needs of the city for 1 day For 1 yr The amount of coal needed in a day is kg

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