# Homework Help: Carbon emissions question

1. Mar 6, 2016

### theone

1. The problem statement, all variables and given/known data
Using the above result, estimate the annual CO2 emission savings (in kg/yr) associated with replacing one 60W incandescent bulb with one 13W fluorescent bulb, in one typical Canadian household. Do this calculation from “first principles” using the following assumptions:

(The "above result" was the answer to "How many hours per day must the replacement and original light bulb be left switched on (on average over the year) to save a certain amount of money per house". The answer was found to be 4 hours)

- The GHG savings are entirely CO2 and result from the reduced combustion of fossil fuels in electric power plants.Canada’s electrical power generation mix is 23 % from fossil fuels. Assume electricity from other sources (hydro, nuclear and renewable) have approximately zero carbon emissions. The carbon intensity of this fossil fuel usage is 22 g/MJ
- Assume the overall efficiency for the fuel energy to electrical power conversion process is 35 %
- Most light bulbs are located indoors, in an occupied living space. So, the net carbon emissions savings will be approximately zero for six months of the year.

2. Relevant equations

3. The attempt at a solution

so (60-13)= 47W worth of carbon emissions is saved by replacing the bulbs,

47W=47 j/s so

47 j/s * (4hours*3600)s * 22(g /MJ) * (1MJ/10^6J) =

14.9g

since carbon savings is zero for half the year, then 14.9/2

= 7.45g?

I'm not sure where to use the info of 35% or 23%?

2. Mar 6, 2016

### BvU

Hi. Your 4 hours is not 4 hours but 4 hours/day. Dimensional error !

3. Mar 6, 2016

### haruspex

That is rather low. Coal is about 88g CO2/MJth. See e.g. https://en.wikipedia.org/wiki/Emission_intensity.
The 22g/MJ is for thermal energy (22g CO2/MJth). Light bulbs need electrical energy. The conversion from thermal to electric is only about 35% efficient.
As against that, only 23% of the electricity used by the bulb will come from fossil fuels.
For each Joule used by a bulb, how many Joules come from fossil fuel electricity? To make that many Joules of electricity from fossil fuels, how many Joules of thermal energy were produced?
I thought the 4 hours/day was already the average over the year.

4. Mar 6, 2016

### BvU

The 22 g/MJ appears to be for fossil fuel used. So divide by the efficiency to get g /MJ electricity generated. That way we agree a bit better with Haru's number.

I also agree with him about the factor 0.5 already in the 4 hours/day calculation -- you could check that with the äbove"calculation !

And if only 23% of the electricity is from fossil fuel, then the savings are only 0.23 of what would be saved if ALL electricty is from fossil fuel...

5. Mar 6, 2016

### BvU

And you get rid of the 1/day by multiplying with days/year, so you end up with something with a dimension of mass/year

6. Mar 6, 2016

### haruspex

No, my 88g is fuel per MJ thermal, so about 300g/MJe, or 1t/MWhe. That's a fairly standard number.

7. Mar 7, 2016

### Tom.G

88g/MJ of fuel could well be correct. However:
is given in the problem statement as a known. Perhaps 22g/MJ is the carbon emitted as smoke, after accounting for scrubbing and ash.

8. Mar 7, 2016

### theone

the actual info from the question was:
"Canada’s fossil fuel based electrical generating capacity is comprised of 70% coal and 30% natural gas (EIA, 2010). Use these percentages to compute the weighted-average carbon intensity, based on the LHV of the three fuel sources given in the class notes"
From the notes: LHV Carbon Intensity (gC/MJ) of natural gas is 15.3, petroleum is 20 and coal is 25.8"

so I did (25.8*0.7)+(15.3*0.3) to get 22.65 gC/MJ.
was that right?

9. Mar 7, 2016

### haruspex

Not sure what this gC/MJ actually means. I can't find it defined anywhere. The worry is that when we talk about greenhouse gas emissions it's always in terms of equivalent CO2 mass. But one gram of C produces about 3.5 g CO2.
The table at http://cta.ornl.gov/bedb/appendix_a/Lower_and_Higher_Heating_Values_of_Gas_Liquid_and_Solid_Fuels.xls [Broken] shows 24g anthracite per MJ. According to https://en.m.wikipedia.org/wiki/Anthracite, anthracite is about 75% carbon, so that's 18gC/MJ, or 65gCO2/MJ.
As I posted, around 80gCO2/MJ heat is the figure I'm familiar with.

Last edited by a moderator: May 7, 2017
10. Mar 7, 2016

### Tom.G

Yes, the math and the approach are right, from the way I understood the given information.

However, as haruspex pointed out, there is the question of is it "Carbon" or "CO2" indicated in the original problem statement. Your OP says "CO2" and the "first principles" clause may indicate that calculation of CO2 is expected. So it looks like you need that one extra step.