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 ($H_2$) and carbon-dioxide ($CO_2$) which is a "green house gas" (GHG). If we care about reducing $CO_2$ emissions we'd need to know the relative amounts of carbon-dioxide emissions of each fuel.

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.

See HW review.

 

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

$$2\,C_8H_{18} + 25\,O_2 \to 16\,CO_2+18\,H_2O$$ Atomic weight of...
  • 2 octane molecules = ?? (2*$C_8$) 16*12g + (2*$H_{18}) 36*1g = 228g
  • 16 carbon dioxide molecules = (16 Carbon and 32 Oxygen atoms)
    16*12g + 32*16g = 704g

So, __704__ g of $CO_2$ are produced for every __228__ g of gasoline

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

$$ \frac{704g\ CO_2}{228g\ C_8H_{18}}* \frac{1g\ C_8H_{18}}{10.8\text{ Calories}}=0.29 \text{g of }CO_2 / \text{ 1 Calorie}.$$

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

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

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

$$\frac{44\text{g }CO_2}{16\text{g }CH_4}*\frac{1\text{g } CH_4}{13.3 \text{Cal}}= \frac{44*1}{16*13.3}=0.21 \text{g of }CO_2 / \text{ 1 Calorie}.$$

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

$$C + O_2 \to CO_2$$ Atomic weight of...
  • Coal = 12g
  • 1 Carbon dioxide = 44g

We want grams of $CO_2$ / Calorie:

$$\frac{44\text{g }CO_2}{12\text{g }C}*\frac{1\text{g } C}{6.5 \text{Cal}}= \frac{44*1}{12*6.5}=0.56 \text{g of }CO_2 / \text{ 1 Calorie}.$$

 

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

Fuel$CO_2$ emissions (g/Cal)
hydrogen 0.0
natural gas (methane) 0.21
gasoline (~octane) 0.29
coal (~ pure carbon) 0.56

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. (Not exactly the same numbers as below...) Make sure you can do the calculation of cost/energy from the numbers in the table below and get the same answer.


[Tcf = 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 with time, 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.

With coal, the price is quite different depending on the energy content of the coal. So, do find both a price (per short ton) for coal as well as the energy content of your kind of coal to use in calculating the cost per million BTU.

Finally, for each of your price sources, include a URL to the page you referenced, and write a sentence or two about the credibility of the website.

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)