# Energy and Power (Full Lecture)

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### Energy and Power (Full Lecture)    if it kicks you in a critical portion of your anatomy Let’s try some basic unit conversions Consider a quarter horsepower of motor In units of watts, this motor would have a power rating of 746 divided by four or 186.5 watts Consider a motor that delivers 560 watts In units of horsepower, this motor has a power rating of 560 over 746 or roughly .75 horsepower Most likely this is a three-quarter motor horsepower Let’s now try an energy, power, and time example necessitating some intermediate unit conversion Consider a two-horsepower motor being used for a span of three hours How much energy in units of joules will it deliver? A two-horsepower motor would have a power rating of two times 746 watts or 1,492 watts or roughly 1.5 kilowatts Three hours represents a span of three times 60 times 60 or 10,800 seconds Energy is power times time 1,492 watts times 10,800 seconds yields 16,113,600 joules or roughly 16.1 megajoules You’ll note that for applications like this, joules are tiny, tiny, annoying, and unwieldy units For this reason, numerous applications make use of a far more convenient unit of energy, the kilowatt hour Pay special attention to the kilowatt hour since in my experience, it presents one of the biggest sources of confusion for those with difficulties distinguishing between the concepts of energy and power The kilowatt hour is a unit of energy It is not a unit of power I know it has a kilowatt in there which is a unit of power, but look at it, it is kilowatts times hour or power times time I say again that kilowatt-hour is a unit of energy It is not a unit of power If you don’t believe me, unwrap each piece of the kilowatt hour one by one and prove it to yourself If one k equals 1,000, one kilowatt hour equals 1,000 watt hours If one watt equals one joule per second, one watt hour equals 1,000 joules per second times one hour If one hour equals 60 minutes, and one minute equals 60 seconds, one kilowatt hour is 1,000 joules per second times 3,600 seconds or 3,600,000 joules In summary the kilowatt hour is a unit of energy It is a unit of power, the kilowatt, times the unit of time, the hour Energy is power times time The simplicity of expressing energy in units of kilowatt hours cannot be overstated Consider a four-kilowatt solar ray being exposed to peak sunlight for a period of four hours How much energy does this solar ray produce in units of kilowatt hours? Energy is power times time Rather than converting hours to seconds as we did when calculating energy using units of joules We simply multiply the power in units of kilowatts times the time in units of hours Four kilowatts times four hours yields 16 kilowatt hours It really is that easy If you wanted to go to the trouble, which I have no idea why you would, you could convert this to joules where one kilowatt hour equals 3.6 megajoules, and 16 kilowatt hours would equal 57.6 megajoules You know calculating energy in units of kilowatt hours is astoundingly easy Oftentimes the wattage or power of a particular device is directly specified in the device’s nameplate All you need to do to determine the energies of a particular device is the number of hours you plan on using it For example, considering an 800-watt air conditioner To calculate the daily energy consumption of this air conditioner, simply multiply the wattage rating by the number of hours you use it everyday An 800-watt air conditioner used for eight hours a day uses 800 times eight or 6,400 watt hours of energy or 6.4 kilowatt hours of energy If however you left the 800-watt air conditioner on all day or 24 hours, you’d be billed for 800 times 24 or 19,200 watt hours or 19.2 kilowatt hours of energy Consider a 100-watt incandescent bulb used for eight hours a day This bulb uses 100 times eight or 800 watt hours of energy or .8 kilowatt hours of energy If you were lazy and you left it on all day or for 24 hours, you’d be billed for 100 watts times 24 hours or 2,400 watt hours or 2.4 kilowatt hours of energy Consider a more efficient 20-watt LED light bulb used for eight hours a day This bulb would use 20 watts times eight hours or 160 watt hours of energy or .16 kilowatt hours of energy If you left it on all day or for 24 hours, you’d be billed for 20 watts times 24 hours or 480 watt hours of .48 kilowatt hours of energy Compare and contrast these last two examples The 100-watt incandescent bulb used five times as much energy as the 20-watt LED light bulb even though they operated for the same length of time It makes sense More power times the same time necessitates more energy even though they are producing the same functional product, namely light of a given intensity Be aware that I’m not so naive to suggest that an LED will be sufficient for all tasks requiring light of a certain quality, let’s say painting a picture or some alone time with your imaginary girlfriend, but I’m confident enough to say that if you simply require light in its most basic form, let’s say task lighting in a factory or to light up your front steps so you don’t bust your ass falling down them, it’d be foolish to use an incandescent bulb to do so principally ’cause the long-term energy cost Additionally compare and contrast the usage patterns Any appliance regardless of type used for 24 hours a day necessitates more energy than an identical device used for only eight hours a day It makes sense Same power more time necessitates more energy This explains why it’s a good economic practice to, one, use efficient devices, i.e., devices that accomplish the same task using less power, and two, use these devices only when it’s necessary, i.e, don’t leave a light on if you don’t need it When you get right down to it, energy is money The more energy you use, the more you pay Nationally, price per kilowatt hour of energy varies depending upon your location from a low of around eight cents per kilowatt hour in regions of the Pacific Northwest, to a high of around 35 cents per kilowatt hour in Hawaii, with a national average of around 12 cents per kilowatt hour at the time of this recording An average house might consume around 30-kilowatt hours of energy daily, although daily energy consumption patterns vary widely from the seven-bedroom McMansions of Salt Lake City chugging 100 kilowatt hours a day, whereas an efficient well-designed modern house with a reasonable number of ecologically and economical conscious people might consume only 10 kilowatt hours Also if you’re on a region characterized by cold winters and temperate summers like Maine or Wisconsin, you might expect larger daily energy consumption in the winter and less in the summer Conversely, if you’re in a region characterized by extremely hot summers and temperate winters like Arizona or Southern Cali, you might expect larger daily energy consumption in the summer and less in the winter Let’s just go with this average daily energy consumption of 30 kilowatt hours per day Given this average price per kilowatt hour and the average amount of kilowatt hours used per day, it’s easy to determine the average cost of energy per day 12 cents per kilowatt hour times 30 kilowatt hours per day yields an average daily cost of \$3.60 and an annual cost of 360 times 365 or \$1,314 per year Given this average daily energy consumption, let’s now take a look at the average power consumption of a typical home If power is energy over time, you might be tempted to think that a house would steadily draw 30 kilowatt hours divided by 24 hours or 1.25 kilowatts, but you would be absolutely wrong Some periods of a day necessitate massive consumption of power For example in the morning when everyone’s waking up, taking a shower, cooking breakfast, and getting ready for the day This brief period of high power consumption is followed by a longer period of lower power consumption when everyone’s at work or school This period is then followed by another burst of high power consumption when everyone gets home and air conditioners, stoves, washers and dryers start chugging power in massive quantities Finally the day draws to a close and the occupants of the house go to sleep, only the water heater and refrigerator continue to draw power Instantaneous power demand peaks and valleys and peaks and valleys, yet we can say there exists some average power demand which happens to be around 1.25 kilowatts such that over the course of a 24-hour period, the house ultimately consumes 30 kilowatt hours of energy Those of you with a calculus background will realize that the energy is the integral or area under the power curve, i.e., power times time The instantaneous power curve can be a little tricky to calculate, so that’s why the average is used If you squinch your eyes just right, you’ll note the overrepresented areas in the early morning and late evening are counterbalanced by the under-representation or morning and afternoon If you multiply the average power figure of 1.25 kilowatts by 24 hours, you realize the energy or area under the power curve is 1.25 times 24 or 30 kilowatt hours Don’t get too stressed about the details of this particular example just yet, but rather think of the large point I’m trying to make Power is instantaneous whereas energy is consumed over time Power is the instantaneous rate of change of energy whereas energy is power consumed over time Let’s try an illustrated example of this concept, focusing in on a single household appliance Consider a water heater that over the course of one year or 365 days is known to consume 4,380 kilowatt hours of energy, given the price of 12 cents per kilowatt hour, what’s the annual cost of using this water heater? Additionally what’s the average power consumption of this water heater? Calculating the annual cost is easy 4,380 kilowatt hours times 12 cents per kilowatt hour yields an annual cost of \$525.60 Average power should be easy too Power is energy over time One year is 365 days, one day is 24 hours, so one year is 8,760 hours 4,380 kilowatt hours over 8,060 hours use a power rating of .5 kilowatts or more appropriately 500 watts You might reasonably think a water heater continuously steadily draws 500 watts of power and could be powered by a 500-watt generator This, however, is an average power figure only, and totally misrepresents how an actual water heater works Water heater don’t heat water continuously but rather in bursts As a simplified explanation, if water in the tank falls below a certain low value, but heater is applied at full blast until water in the tank has risen above a certain high value, after which the heater is completely turned off and the tank’s insulation, thermal inertia of the water, temporarily hold it inside a specified range The result is a periodic full-on, full-off, bang-bang style control that only on average consumes 500 watts In reality we might expect the water heater to briefly consume massive amounts of power during the heat phase, and then simply turn off during the rest phase until the temperature in the tank falls below the reset value Obviously water usage patterns would influence this periodic cycling As a simplified illustration of this process, let’s say a four-kilowatt water heater operates in a 12 1/2% duty cycle where for 12 1/2% of 60 minutes or 7 1/2 minutes, the four-kilowatt heater runs at full blast, and the remaining 87.5% of 60 minutes of 52.5 minutes, the heater is completely off What you’d experience over the day is regular burst of four-kilowatt power demand followed by an idle state If you summate the on times for a 24-day, i.e., 24 times 7 1/2 minutes or 180 minutes or there hours, it means a four-kilowatt device has been used for a total of three hours or a daily consumption of four kilowatts times three hours or 12 kilowatt hours If the water heater did this everyday for 365 days, it would consume 365 times 12 kilowatt hours or 4,380 kilowatt hours of energy annually Additionally you’d need that minimum of four-kilowatt generator to power this water heater when it was on That generator only working 12 1/2% of the time, and the other time it would sit idle Again those of you with a calculus background will realize energy is the area under the power curve Rather than using instantaneous periodic power burst however, it’s perhaps easier to simply use the average power figure of 500 watts over the 24-hour period which yields 12 kilowatt hours of energy per day Moving on, returning to our discussion of units employed when quantifying energy, the kilowatt hour makes a handy unit for most small scale residential applications However, if the application is smaller in nature like a portable electronics device or sometimes batteries, you might alternatively see units of energy represented in watt seconds or watt hours Watt second is simply a stupid way of writing a joule because one watt times one second is one joule per second times a second which yields joules And a watt hour is a larger packet of joules If one hour equals 3,600 seconds, a watt hour is 3,600 joules, or more appropriately 3.6 kilojoules For example consider a storage battery known to have an energy capacity of 600 watt hours,   