Simple energy calculation help

[bgizzle]

Hi,

I'm trying to calculate theoretical energy generated by a system and I'm not sure if I'm doing it right and if I understand the concept properly. Here is my thinking, any input is appreciated.

12 billion joules of energy generated over 1800 seconds

equals roughly 6.8 million watts by dividing 12 billion by 1800

6.8 million watts * 8765 hours in a year = 60 billion watt hours/year

or is it .00027777*12 billion joules=3.5 million watt hours then 3.5 million * 8765 hours in a year = 30 billion whr/year

so basically i have joules of energy generated over a period of time, how do I convert that into total energy generated over the course of a year. I'm struggling with how to properly translate the different time periods into standard units of energy.

Appreciate any help.

 

[deep838]

Okay, first of all, is it so hard for you to work using powers of 10? Or do you like to writing big?

Now, you have some energy (W) which you have generated in a period of time (t) and hence you can find the power (P) generated, by P = W/t , ie, P = 12*10⁹J / 1800 sec, ie, P = 6.67*10⁶ watt.

If you need the energy created in a year, just multiply P with one year in seconds...
1 year = 365*24*60*60 sec = 3.1536*10⁷ sec

So the net energy produced in a year, E = P*3.1536*10⁷ sec, ie, E = 2.1024*10¹⁴ J.

If you want it in watt.hr^-1.yr^-1 then your first answer should be alright. But in your second answer, what is 0.00027777 you are multiplying with? I don't think its correct and so you are getting two different answers!

 

[bgizzle]

So how do I convert your joule number of 2.1024x10^14 to watt hours per year properly?

the first part of your calculation is in watts: 6.67*10^6 but when you multiplied it by seconds in a year your result was in joules, is that right?

lol, sorry for some reason I like big numbers.

 

[mfb]

1W*1yr =1W*3.14*10⁷s = 3.14*10⁷*W*s = 3.14*10⁷ J
Just convert units, there is no need to multiply any value with another value.

 

[bgizzle]

1W*1yr =1W*3.14*10⁷s = 3.14*10⁷*W*s = 3.14*10⁷ J
Just convert units, there is no need to multiply any value with another value.

If I understand you correctly (doubtful) then I divide 12 billion joules by 1800 seconds and get 6.8 million watts which i then multiply by 3.14*10^7 to get watt hours per year which i then divide by 1,000,000,000,000 to get twh/year of 217. I'm pretty sure that is wrong but hoping its right.


I'm not sure I understand (I have no formal physics background), at this point I am pretty thoroughly confused. I would like to know: 12 billion joules of energy generated over 1800 seconds would lead to how many terawatt hours generated over the course of a year. Without a firm answer or a very comprehensive explanation I cannot reverse engineer it so I can understand it. If you would like to change the original joules and seconds that is fine.

Thanks for your post.

 

[etudiant]

Hi bgizzle,
I think you would want to give mbf and deep838 credit, they show you the answer but do keep it compact.
You have 12x10**9 joules in 1.8x10**3 seconds is 6.8x10**5 watts.
You have 3.1536x10**7 seconds/yr, so you generate overall 6.8x3.1536x10**12 watts each year.
Divide that by 3600sec/hr and again by 10**12 and that is your terawatt hours/year.
The key is to keep good track of the dimensions, joules measure energy, watts measure energy/second ie power. That is why dimensions such as terawatt hours/year are really ambiguous and confusing. They simplify the language but confuse the realities of the matter.

 

[bgizzle]

Hi bgizzle,
I think you would want to give mbf and deep838 credit, they show you the answer but do keep it compact.
You have 12x10**9 joules in 1.8x10**3 seconds is 6.8x10**5 watts.
You have 3.1536x10**7 seconds/yr, so you generate overall 6.8x3.1536x10**12 watts each year.
Divide that by 3600sec/hr and again by 10**12 and that is your terawatt hours/year.
The key is to keep good track of the dimensions, joules measure energy, watts measure energy/second ie power. That is why dimensions such as terawatt hours/year are really ambiguous and confusing. They simplify the language but confuse the realities of the matter.

Ok, thanks for your response, not sure why you think I wasn't giving them credit. So if I understand you correctly the final answer is approximately .06 twh/year (6.0x10^-2). You multiply in all the seconds in a year but then divide out the seconds in an hour to get the units in terms of watt hours/year.

 

[deep838]

So how do I convert your joule number of 2.1024x10^14 to watt hours per year properly?
the first part of your calculation is in watts: 6.67*10^6 but when you multiplied it by seconds in a year your result was in joules, is that right?

Of course it's right... Watt is Joules/sec, so on multiplying Watt with sec, I get back to Joules!

If you need watt-hrs, which by the way is also energy, just multiply P with 1 hr...
And then if you need watt-hrs/yr, which is again power, multiply with the number of hours in 1 yr and then divide P*365*24 hr by 1 yr...
Conversion from one unit to the other is not a special facility for physics, its just mathematics... more of arithmetic actually. Only the terms and names if the units come from physics in this case!

 

[deep838]

Hi bgizzle,
...
You have 3.1536x10**7 seconds/yr, so you generate overall 6.8x3.1536x10**12 watts each year.
...

No, that's not watt/yr ! That's Joules/yr !

Because 1 watt is DEFINED to be Joules/sec .

 

[bgizzle]

Of course it's right... Watt is Joules/sec, so on multiplying Watt with sec, I get back to Joules!

If you need watt-hrs, which by the way is also energy, just multiply P with 1 hr...
And then if you need watt-hrs/yr, which is again power, multiply with the number of hours in 1 yr and then divide P*365*24 hr by 1 yr...
Conversion from one unit to the other is not a special facility for physics, its just mathematics... more of arithmetic actually. Only the terms and names if the units come from physics in this case!

Ok, thanks for all your help. I believe I understand it now.