Calculating kilowatt hours concerning a toaster

[PeachBanana]

Homework Statement

2 part problem

How many kWh of energy does a 650-W toaster use in the morning if it is in operation for a total of 20min?

At a cost of 9.0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

Homework Equations

None really, just a lot of conversions.

The Attempt at a Solution

Part A:

650 W = .650 kW
0.650 kW(.33 hr) = 0.2145 khW

Part B:

(0.2154 kWh)(5.28 hr)(0.09 kWh) = .10

I know that sounds really low but I'm unsure of my error.

Here's how I found 5.28 if it matters.

(0.33 hr)(16 times/month) = 5.28 hr

 

[voko]

First of all, I would use .333 hr for 20 minutes. Second, see that you use .33 TWICE - first when you compute daily consumption, then the monthly consumption. That's not right. Finally, 16/4 may be too inaccurate. You would get a far more accurate estimate if you take the number of weeks in a year, then get how many days in a year you would use the toaster, and then divide that by 12.

 

[PeachBanana]

I still don't understand. I don't think I followed your directions properly because now I get 0.11 as an answer.

0.333 hr/1 day * 4 days/week = 1.332 hrs/1 week * 52 weeks/1 year

69.264 hrs/1 year * 1 yr/192 days = 0.36075/1 day

I didn't divide that last number by 12 because it seemed too small. Sorry if that is not what you meant.

(0.2154 kWh)(5.772 hrs)(0.09 kWh) = 0.11

(0.36075 hrs/day)(16 days) = 5.772 hrs

 

[voko]

How many days in a year would you use the toaster if you use it four times a week?

 

[PeachBanana]

192 days/year.

So along the lines of:

0.36075 hours 192 days
-------------|-----------= 69.264 hours/year
1 day 1 year

(0.2145 kWh)(69.264 hours)(0.09 kWh) = $1.337/year (I only typed year based upon the number of hours)

1.337
------= 0.111
12

 

[voko]

The toaster is used 192 days a year, that's correct.

But then you multiply by .36075? Where does this number come from? You should multiply by the daily duration of the toaster use. What i it?

Once you have total yearly duration of the toaster use, what is the energy consumed?

 

[cepheid]

Aren't we way overcomplicating this? If the toaster consumes 0.2154 kWh of energy during each use, how much energy is consumed after 4 (edit: I mean 16) uses? How much does that cost?

 

[voko]

16 days a month is about 8% undervalued. .2145 kWh is about 1% undervalued (which is somewhat offset by the fact that even though .2145 was computed, .2154 was then erroneously used throughout). So all together it would be almost 10% undervalued, which seems too much.

 

[PeachBanana]

cepheid - I know that's how I thought you were supposed to do this problem but MasteringPhysics won't accept my answer.

voko - I'm not sure how the energy consumed will lead me to the cost/mo.

(0.333 hr) (192 days)
---------| -------- = 63.936 hours/year
1 day 1 year

(0.2145 kWh)(0.09 cents/kWh)(63.936 hrs) = $1.2428/year

If I divide that number by 12, I keep getting an answer within the same range as my previous ones. Is the answer you get completely different than 0.10 or 0.11?

 

[cepheid]

I have no idea what you guys are on about.

As voko pointed out, your numbers are slightly off. You get 0.2145 kWh, but the true answer is closer to 0.21667 kWh. The discrepancy is due to rounding error. You used 0.33 hr when you should have used 1/3 hr. Multiplying by 1/3 is the same as dividing by 3, so just *do that* on your calculator. Or equivalently, multiply by 0.333333333 with a lot of decimal places to avoid rounding error.

Secondly, there is the issue of determining how many times then toaster is used in a month. As Voko pointed out, just assuming 4 weeks per month, for a total of 16 uses, is an underestimate, since most months have more than 28 days in them, so on average, you might use the toaster one or two more times than 16 in a month. So that's why figuring out the number of uses in a year and dividing by 12 is better. But I don't understand your numbers there either! There are 52 weeks in a year, so if you use the toaster 4 times a week, that's 52*4 = 208 uses in a year. NOT 192. I don't know where you got 192 from. Anyway, if I divide 208 by 12, I get an average of 17.3333333 toaster uses per month. So that's a bit more than 16.

The thing is, *regardless* of whether I use 16 or 17.33333 in my calculations, I don't get a final answer that is anywhere near 10 cents. My final answers are larger than that. I don't know what you're doing, but somethig is screwy with your arithmetic. You need to double check it.

 

[voko]

(0.333 hr) (192 days)
---------| -------- = 63.936 hours/year
1 day 1 year

Now that you have total time and you know the power of the toaster, how do you compute the energy used by the toaster, and the price of that energy? When you do so, that will be your annual bill - convert that to the monthly bill.

(0.2145 kWh)(0.09 cents/kWh)(63.936 hrs) = $1.2428/year

This is wrong on two accounts.

1. You multiply the total number of hours by .2145 kWh. But the latter already has the time duration in it, it is the product of power and daily use time. That's the biggest error in the entire computation.

2. 0.09 is in dollars, not cents.

 

[cepheid]

(0.2145 kWh)(0.09 cents/kWh)(63.936 hrs) = $1.2428/year

It's this here that is the problem. It's just totally wrong. I don't know what you're doing here.

Think about it: 0.21667 kWh is the energy used PER toasting session. So to get the total energy used, you just need to multiply by the total *number* of toasting sessions. You shouldn't be multiplying by a time interval: that 63 hrs should not be there. You already multiplied the power by the time in part a) to get energy. You don't need to do it again.

 

[CWatters]

1) How many kWh of energy does a 650-W toaster use in the morning if it is in operation for a total of 20min?

Energy(kWh) = power(kW) * time(hrs)
= 0.65 * 20/60
= 0.2167 kWh

eg not 0.2145 kWh

2) At a cost of 9.0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

The problem here is that the length of a "month" varies. Best calculate the annual consumption and divide by 12 to get the average monthly cost..

Monthly_cost($) = Weekly_cost($) * number_of_weeks_in_a_year / number_of_months_in_year

Weekly_cost($) = cost_per_kWH($) * number_of_kWH_per_morning * number_mornings_per_week

So

Monthly_cost($) = cost_per_kWH($) * number_of_kWH_per_morning * number_mornings_per_week * number_of_weeks_in_a_year / number_of_months_in_year

= 0.09 * 0.2167 * 4 * 52/12
= $0.338
Call it $0.34

 

[PeachBanana]

Ok. The very first time I had done this I was much closer because my answers were coming out to be ~0.30. I think there's problem with MasteringPhysics because I entered in 0.34 as an answer which it told me was wrong. We've been having issues with it lately. Thank you for the help and I hope I don't struggle this much on future problems haha.