Week One Solutions
Basic thermal physics and chemistry
1. In 2008 Gordon Campbell introduced BC’s carbon tax of $30 per tonne of CO2e, and the
intention was that this rate would rise with time as we made the transition to a carbon-free
economy. In fact the rate has been frozen, while we still trumpet our climate leadership to the
world. Economic modellers reckon the rate will need to rise at the rate of $10/tonne/year until
2050 if we are to meet our mid-century carbon targets.
What would a tax of $100/tonne do the price of a litre of gasoline (≈ CH2)? Show your working.
Assume an instantaneous change, i.e. ignore any response of the general economy.
NO NEED TO HAND THIS IN, BUT HERE IS THE SOLUTION ANYWAY:
CH2 + oxygen -> CO2 + water*
14
44
1L of gasoline has a mass of 0.8 kg, which will burn to 44/14 x 0.8 kg = 2.5 kg/L of CO2. At
$100/tonne this will cost ($100)(2.5 kg/L/1000 kg) = $0.25/L
For considering the change in cost over the present $30/tonne: $70/tonne will cost $0.175/L
* A very subtle point is that water vapour is a GHG but doesn’t count as “CO2e” at low levels
(becomes part of “weather”). It does count at high altitude (air travel emissions).
2. We Canadians each waste about 100 kg of food carbohydrates per year. If these carbohydrates
are composted anaerobically, half the carbon atoms end up as carbon dioxide (CO2) and half end
up as methane (CH4).
The energy needs of a small single-family dwelling is typically 0.3 GJ per day averaged over a
year. How long could such a house be supplied with energy from composting 100 kg of
carbohydrates?
The approximate ratio of carbon, hydrogen and oxygen atoms in carbohydrates, C:H:O, is 1:2:1.
The enthalpy of combustion of CH4 (i.e. the “energy content”) is about 55 MJ/kg.
The decomposition of carbohydrates can be represented by the chemical formula, which can be
deduced from the information that half the carbon atoms end up in carbon dioxide and half in methane:
2CH2O → CO2 + CH4
Energy can thus be extracted from composted carbohydrates by collecting and burning the methane.
2CH2O → CO2 + CH4
60
44
16
By adding the atomic masses given, we can use this formula to find that 60 kg of carbohydrates yield 16
kg of methane, and so 100 kg of carbohydrates would yield (100/60)(16) = 26.67 kg of methane.
To find the energy generated by this mass of methane, we multiply it by the enthalpy of combustion.
55 MJ
(26.67 kg)(
) = 1467 MJ = 1.467 GJ
kg
If a house need 0.3 GJ/day, then 26.67 kg of methane can supply this for a time period T, given by:
𝑇=
1.467 GJ
= 4.89 Days
0.3 GJ/day
The energy generated from the methane would last a household approximately 5 days.
Note: whilst it is good to recover any useful energy that would be wasted, it is obviously better not to
waste it in the first place. The ratio of embodied energy to food energy varies from a horrible 75 for beef
to a not bad 0.35 for corn (and that is before you drive home from Safeway and cook it). Or to put it
bluntly:
“Agriculture is the means by which oil is turned into food”
Ref: Roger Hinrichs, “Energy, its use and the environment” 2nd ed., p. 550 (1996).
3. On November 29, 2016, the Government of Canada granted approval for the Trans
Mountain Expansion Project which will have the capacity to move 890,000 barrels of oil
(140,000 m3) per day from Edmonton, AB to Burnaby, BC. The hydrocarbons to be
transported – diluted bitumen and oils - have a typical density of 0.9 tonnes/m3 and a
carbon content of 90% by mass.
When this material is delivered to customers and burnt, estimate how many tonnes of carbon
dioxide (CO2) per year will be dumped in the atmosphere as a result. Assume the pipeline
operates at full capacity, and no carbon is lost except by burning.
Note: Occasionally end-users employ small-scale carbon capture and storage, but this is mostly
to produce CO2 for industrial use or for soft-drinks, and thus the CO2 will end up in the
atmosphere anyway.
NO NEED TO HAND THIS IN, BUT HERE IS THE SOLUTION ANYWAY:
-
140,000 m3 of dilbit weighs 126,000 tonnes:
140,000 m3 ∗
-
0.9tonnes
= 126,000 tonnes𝑑𝑖𝑙𝑏𝑖𝑡
m3
126,000 tonnes of dilbit contains 113,000 tonnes of carbon:
126,000 tonnes𝑑𝑖𝑙𝑏𝑖𝑡 ∗ 90% = 113,000 tonnes𝑐𝑎𝑟𝑏𝑜𝑛
-
Now that we know the mass of carbon that is being transported per day, we must
calculate the mass of carbon dioxide (CO2) that corresponds to 113,000 tonnes of
carbon. Knowing the atomic mass of oxygen (16) and of carbon (12), we can calculate
the atomic mass of carbon dioxide:
(1 carbon) ⋅ 12 + (2 oxygen) ⋅ 16 = 44
From this calculation we can see the ratio of proportionality between the carbon and
the entire mass in CO2. Since there is only one carbon in the molecule, the ratio of
proportionality is:
(Atomic Mass of CO2 ) 44
=
(Atomic Mass of C)
12
Then we know that 113,000 tonnes of carbon are equivalent to 415,800 tonnes
of carbon dioxide:
44
113,000 tonnes𝑐𝑎𝑟𝑏𝑜𝑛 ∗
= 415,800 tonnes𝐶𝑂2
12
Now that we know the mass of carbon dioxide that is going to be dumped in the
atmosphere per day, we just have to multiply the answer by 365 day in a year to
get the yearly mass:
415,800
tonnes𝐶𝑂2 365 days
𝐭𝐨𝐧𝐧𝐞𝐬𝑪𝑶𝟐
⋅
= 𝟏𝟓𝟏, 𝟕𝟔𝟕, 𝟎𝟎𝟎
= 𝟏𝟓𝟐 𝐌𝐭𝐨𝐧𝐧𝐞𝐬/𝐲𝐞𝐚𝐫
day
year
𝐲𝐞𝐚𝐫
This amount represents an additional 27% to Canada’s annual national CO2
production (2015 numbers) – and all from one pipeline.