Combustion comparison

To generate electricity you need a certain amount of heat to boil water and drive a steam turbine. But you can get that heat from many different sources, including coal, natural gas, nuclear power. The choice depends on cost and effect on the environment.

Most of the fuels currently in use are fossil fuel hydrocarbons : molecules containing a mixture of carbon and hydrogen. Burning these in air (which contains oxygen) produces mostly water vapor ($H_2O$) and carbon-dioxide ($CO_2$) which is a "green house gas" (GHG). If we care about reducing $CO_2$ emissions, it seems like the fuel that generates the most energy with the least $CO_2$ would be the best. Calculate that for a couple of different hydrocarbons:

In this assignment

• You'll calculate how much $CO_2$ (in grams) is emitted when you *burn* (combust) enough of each type of fossil fuel to give off 1 Calorie (=1 kilocalorie) of heat (thermal) energy.
• You'll also look up the cost of different fuels for the same amount of heat generated.

Combustion worksheet (.PDF)

See HW review and Combustion worksheet (.PDF)

Coal - $~C$ - combustion: 6.5 Calories / gram

• 1 mole of coal = 1 mole of C = 12g
• 1 mole of carbon dioxide = 1 mole of C*(12 g /mole of C) + 2 moles * (16 g / mole of O)= 44 g / mole of $CO_2$.

We want grams of $CO_2$ / Calorie:
$$\frac{\text{[     ]g }CO_2}{\text{[     ]g }C}*\frac{1\text{g } C}{6.5 \text{cal}}= \text{[     ]g of }CO_2 / \text{ 1 Calorie}.$$

Gasoline (av. octane) - $C_8H_{18}$ - combustion: 10.8 Calories / gram

1 mole of $C_8H_{18}$ weighs 8*(12 g/mole of C)+18*(1 g/ mole of H)=96+18=114 g / mole. So...

Atomic weight of...

• 2 moles of octane molecules = ?? 2 moles * 114 g/ mole of octane = 228 grams 16*12g ($C$) + 36*1g ($H_{18}$) = 228g
• 16 moles of carbon dioxide molecules = 16 moles * 44 g / mole of $CO_2$ = 704 g16*12g ($C$) + 16*2*16g ($O_2$) = 704g

So, 704 g of $CO_2$ are produced for every 228 g of gasoline

We want grams of $CO_2$ / Calorie: $$\frac{[...]\text{ g }CO_2}{[... ]\text{ g } gasoline}*\frac{1\text{ g } gasoline}{10.8 \text{Cal}}=[\ \ \ \ \ \ \ \ ]\text{grams of }CO_2 / \text { 1 Calorie}.$$

$$ \frac{704*1}{228*10.8}=0.29 \text{g of }CO_2 / \text{ 1 Calorie}.$$

Natural gas (methane) - $CH_4$ - combustion: 13.3 Calories / gram

$$CH_4 + 2\,O_2\to CO_2+2\,H_2O$$ Atomic weight of...

• 1 methane = ? = $CH_4$: molecular weight = 12g + 4*(1g) = 16g
• 1 carbon dioxide = ? 12g + 2*(16g) = 44g

So, ____ g 44g of $CO_2$ are produced for every 16g____g of methane :

We want grams of $CO_2$ / Calorie:

So now we can compare $CO_2$ emissions for the same heat (in Calories) for different fuels:

Hydrocarbons in transportation

Cost comparison

This page http://tinyurl.com/costofE (from a government agency) contains a table which compares the (heat) energy content of coal, oil, and natural gas. Make sure you can do the calculation of cost/energy from the numbers they provide and get the same answers as in the table below:

2011 Costs of energy for different fuels (\$/million BTU)

[Tcf = thousand cubic feet = 1,000 cubic feet]

Apparently...$$ \frac{\$56.35}{1 \text{ barrel}}\times\frac{1 \text{ barrel}}{6 \text{ million BTU}} = \$9.39 / \text{ million BTU}$$

The number of BTUs for each fuel type doesn't change, but the costs in the table above are out of date.

Scour the Internet to find recent costs of oil, coal, and natural gas. For each price,

• cite the website you used,
• find out and write a sentence or two about the organization behind the website, and write a sentence or two on why you think it's trustworthy.

Then recalculate the table using the current costs you found for each fuel, to get a figure in $ / Million BTUs based on the costs you uncovered. You may need to do further conversions, e.g. on WolframAlpha. Show each calculation with units.

Current prices (2017) are around \$40-50/short ton of coal, \$57 / barrel of oil, and \$3 / tcf. So coal is getting more expensive, oil is staying about the same price, and natural gas has gotten cheaper.

Some common units of energy...
1 Calorie = 1 kilocalorie = 4184 J
1 BTU = 1055.06 J
1 kWh = 3.6 MJ (MegaJoules)

Here are the conversion factors you'll need to calculate the price of coal per mega BTU (million BTU):

The energy content of coal depends quite a bit on the source!

Units are BTU per pound. We need to find mega btu per short ton, so for Northern Appalachian coal: $$\frac{\text{13,000 BTU}}{\text{1 lb}}\cdot\frac{\text{___ lbs}}{\text{___ short ton}}\cdot\frac{\text{1 "million BTU"}}{\text{1,000,000 BTU}}=\frac{\text{___ million BTU}}{\text{short ton}}.$$