Question

This is a fermi problem that we are suppose to learn how to do estimation with, I am stuck on this one question though.

der of this kW 1000 W 11/kWhr. The Here are sone r i are tome relations and numbers that will help you with the rem One watt (W) is In the U.S., the number of kilowatts you consume in utility companies charge consumers at a rate of about 11 is read "kilowatt-hour and it is a unit of energy. As the name s equivalent to expending 1 joule of energy in 1 second. (1 kw- suggests, it is is our. If, for example, you need to use much that 1 h 1800 W hairdryer for 1 will cost you by doing the following... 5 minutes to dry your hair, you can figure out unit conversion: 1800 W-1.8 kW 0.45 kWhrs Energy used: 1.8 ewx 0.25 hrs Cost of energy used: 0.45 kWhrsx $0. 1I so.o5 5 4. (15 points) There are about 600 million television sets in About half of the sets are newer models that operate with.S for use" feature, which means they draw about 40 60 W when they are off. While on, they typically draw about 450 W much does it cost per year to use all the "ready-use" sets while are on? Compare this to how much it costs per year to run these sets while they are off. The other half of the TVs are older models that when they are on, so they draw about 500 W, but when theyare off, they are really "off (meaning they do not draw any power). How much does it cost per year to run all of these older sets? of are less efficient Does it cost more money per year to run all the new models or the old models? Put all of your final dollar amounts in units that you are accustomed to hearing, "hundreds," "thousands," "millions," or whatever

Answer 1

Let's see first the cost of operating new "ready for use" models.

Total number of Tv sets = 300 million= 300,000,000 = 3 X 10⁸

Now as per the stats available, average american watches TV 35.5 hours per week.

Now let's first calculate the total hours in 1 year - hours

Total hours the TV is On = 35.5 X 52 weeks = 1846 hours. Total time the TV is Off = 8760 - 1846=6914 hours

Electricity consumed by 1 TV per hour is 450 W - 450/1000 = 0.45 KW

So the Electricity consumed by 1 TV in 1 year while it is ON

Now the time for which TV is off is 6914 hours. The electricity consumption during off hours is 40-60 W. Let's take 50 W as average for calculation. 50 W = 50/1000 = 0.05 KW

So electricity consumption for 1 TV in 1 year is

Now the cost of 1 KWhr is $ 0.11

Let's calculate the operating cost while the TV is ON -  

Units while the TV is On is 830.7 KWhr . Thus cost per year for 1 TV is

For 300 million TV it is -

Now lets calculate the cost when TV is OFF is -

cost per year for 1 = TV

For 300 million TV it's -

Thus total operating cost of New model TV per year is 11,406 + 27,411 = $38,817 million

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Calculation of operating cost of running older sets

Number of TV = 300 million

Electricity consumed by 1 TV = 500 W = 0.5 KW

Time for which TV is ON in 1 year = 1846 hours

Thus consumption for 1 TV in 1 year =

Annual Operating cost for this TV is =

So the cost of operating 300 million TV per year will be =

Thus total operating cost of Older sets per year is $ 30,459 million

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Comparing the 2 costs above, we can see that running the Older TV is less expensive than running the new ones