Calculating Electrical Energy and Power Costs

In summary, the cost of electricity can vary widely in the United States and is typically around $0.120/kWh. Using this unit price, the cost of leaving a 40 W porch light on for 2 weeks is $1.61, making a piece of dark toast in 3 minutes with a 970 W toaster is $0.01, and drying a load of clothes in 40 minutes with a 5200 W dryer is $0.42. It is important to note that the number of significant figures in the answers should not exceed the number with the least.
  • #1
AznBoi
471
0

Homework Statement


The cost of electricity varies widely throughout the United States; $0.120/kWh is a typical value. At this unit price, calculate the cost of (a) leaving a 40 W porch light on for 2 weeks while you are on vacation, (b) making a piece of dark toast in 3 min with a 970 W toaster, and (c) drying a load of clothes in 40 min in a 5200 W dryer.


The Attempt at a Solution


I have my attempt but I doubt I doing this right because it doesn't make sense at all. Can you please tell me where I'm messing up? Thanks in adv.! :smile:

[tex]a) 40W*\frac{1kW}{1000W} = 0.04 kW[/tex]
[tex] 2 weeks * \frac{7days}{1week}*\frac{24 hours}{1 day}=336h[/tex]
[tex] \frac{0.120}{kWh}*0.04kW*336h= 1.6128[/tex]

Is my method for (a) right? I got $1.6128 and it seems too little.. =[
 
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  • #2
14 days times 40 w; that's 24*14 *.04=13.4 KW-hrs times 12 cents=what you say. Post the rest of the results,I'd be curious.
 
  • #3
I'm not a maths expert, but you're logic seems to make sense, even though the answer is quite small. I worked it out in a similar way to you:

energy transferred or total units (Kw/h) = power (kw) x time (h).

Then

total cost = number of units x cost per unit.

Perhaps, 40W is not a lot of power? The average hairdryer is 1.5kw
 
  • #4
Your answer is correct to part a.

Part of the reason we consume such an enormous amount of resources in the US is precisely because the price of those resources is so low compared to other places in the world. 40W is currently an almost insignificant amount of power in terms of its cost, but this might not always be so.

- Warren
 
  • #5
Thanks for all the replies. =]
As to denverdoc, here's what I got for part b) and c):

[tex]b) \frac{0.120}{kWh}*0.970kW*0.05h= 0.00582[/tex]
b) $0.00582 o_0 is this correct??

[tex]c) \frac{0.120}{kWh}*5.2kW*0.667h= 0.416208[/tex]

b) $ 0.416208
 
  • #6
Thanks. Theres something to be said for air drying ones clothes the old fashioned way.

My only issue I see with the answers are the number of significant figures; rremember that the answer should have no more sig figs than the number with the least:

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html

So answer b should be .01, etc
 
Last edited:
  • #7
denverdoc said:
Thanks. Theres something to be said for air drying ones clothes the old fashioned way.

My only issue I see with the answers are the number of significant figures; rremember that the answer should have no more sig figs than the number with the least:

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html

So answer b should be .01, etc

No problem. =] Thanks for reminding me of the sig figs :smile:
 

1. What is electrical energy?

Electrical energy is a type of energy that is created by the movement of electric charges. It is the energy that powers most modern devices and is essential for our daily lives.

2. How is electrical energy generated?

Electrical energy is generated by converting other forms of energy, such as mechanical, chemical, or solar energy, into electrical energy through various methods such as generators or solar panels.

3. What is the difference between electrical power and energy?

Electrical power is the rate at which electrical energy is consumed or produced, while electrical energy is the total amount of energy consumed or produced over a period of time.

4. How is electrical power measured?

Electrical power is measured in units of watts (W) or kilowatts (kW). One watt is equal to one joule of energy per second, and one kilowatt is equal to 1000 watts.

5. What are the factors that affect electrical energy and power?

The factors that affect electrical energy and power include the amount of voltage, the current, the resistance in a circuit, and the efficiency of the energy conversion process.

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