MD Problem Set 7
pdf
School
University of California, Berkeley *
*We aren’t endorsed by this school
Course
C100
Subject
English
Date
Feb 20, 2024
Type
Pages
8
Uploaded by LieutenantBookGoat28
ER100/PP184/ER200/PP284, Fall 2023
Problem Set #7
Total Points: 100 for ER110/PP184; 125 for ER200/PP284
1)
Sustainable Bioenergy Use
[25 points]:
The DOE billion ton study says that roughly 1 billion tons of biomass can be used
sustainably in the United States. This bioenergy can be used for building heat
(either through direct combustion or through conversion to electricity) and for
passenger vehicles (either through conversion to biofuel or electricity). Determine
the most efficient use of limited bioenergy resources.
Assumptions:
●
efficiency of converting biomass to electricity is 30%
●
efficiency of converting biomass to biofuel is 60%
●
efficiency of battery electric vehicle is 85%
●
efficiency of biofuel combustion vehicle is 25%
●
efficiency of heat pump is 300%
●
efficiency of wood furnace is 70%
●
1 ton of biomass contains 13*10^6 BTU
a)
What is the efficiency (%) of directly burning biomass for heat? What is the
efficiency (%) of converting biomass to electricity, then using that electricity to
power a heat pump? [5 points]
Direct Burning for Heat: The efficiency is given as 70%.
Converting to Electricity for Heat Pump:
Biomass to electricity conversion efficiency is 30%.
Efficiency of a heat pump is 300%.
Total efficiency =
0.30×3.00=0.90
0.30×3.00=0.90 or 90%.
b)
What is the efficiency (%) of converting biomass to biofuel, then using that fuel
to power a combustion vehicle? What is the efficiency (%) of converting biomass
to electricity, then using that electricity to power an electric vehicle? [5 points]
Biomass to Biofuel for Combustion Vehicle:
Conversion of biomass to biofuel efficiency is 60%.
Biofuel combustion vehicle efficiency is 25%.
Total efficiency =
0.60×0.25=0.15
0.60×0.25=0.15 or 15%.
Biomass to Electricity for Electric Vehicle:
Biomass to electricity conversion efficiency is 30%.
Battery electric vehicle efficiency is 85%.
Total efficiency =
0.30×0.85=0.255
0.30×0.85=0.255 or 25.5%.
c)
What does this analysis ignore? List at least three factors. [10 points]
Environmental Impact: The impact of biomass harvesting and processing on the
environment and biodiversity.
Distribution and Transmission Losses: Energy losses in the process of distributing
and transmitting electricity or biofuel.
Resource Availability and Scalability: Availability of biomass in different regions and
the scalability of biomass production and processing.
Lifecycle Emissions: The total greenhouse gas emissions across the lifecycle of
biomass production, processing, and usage.
d)
If the total energy required for building space heat in the U.S. is 7*10^18J and
total energy required for passenger vehicle transport is 16*10^18J, then what
percent of building space heat and passenger vehicle transport respectively could
be met by bioenergy? [5 points]
2)
Lithium Batteries [25 points for undergrad, 35 points for graduate]:
a)
Let’s assume that a first-generation Tesla Powerwall is made up of battery cells
that use graphite (C
6
) in the anode and lithium cobalt oxide (LiCoO
2
) in the
cathode. Assume each cell’s capacity is 2.7 Ah and has a voltage of 4.4 V. If the
Powerwall’s total storage capacity is 7.00 kWh, how many cells are there? What
is the total mass of anode (kg) and cathode (kg) material in the Powerwall?
Assume that the energy content of 1 gram of graphite is 370 mAh/g, and the
energy content of 1 gram of LiCoO
2
is 137 mAh/g. You may find it useful to
review the materials from Section 10 for this problem. [10 points]
each cell capacity 2.7Ah / 4.4 V
energy stored = 2.7*4.4 = 11.88 Whr
Powerwall storage = 7.0 kWh
number of cells required = 7.0E+3 / 11.88 = 589.22
we need 590 cells.
energy content of 1 gm of Graphite (cathode) = 137 mAh
1 gm of LiCoO2 (anode) = 137 mAh
2 gm of battery weight gives us 131 mAhweight of each cell = 2.7/137E-3 = 19.71
gm
Weight of Powerwall battery = 19.71* 590 gm = 11.63 kg
b)
How many lithium ions are in the Powerwall? What is the mass (in grams) of lithium
per Powerwall? Assume 1.0 lithium ion per unit charge (100% of lithium atoms go
through the oxidation reduction reaction) and the molar mass of lithium is 6.94 g/mol.
One unit charge (q) is 1.6x10
-19
coulombs, and one coulomb is one Ampere-second. [10
points]
1 Li-ion gives 1.6E-19 Columbs of charge = Amp-s
one cell outputs 2.7 Ah
Li- ions in one cell = 2.7*3600/ 1.6E-19 = 6.075 E+22
Powerwall contains = 6.075E+22 * 590 = 3.584E+25 Li ions
molar weight of Li - 6.94 gm
1- mole contains 6.02 E+23 atoms (Avogadro number)
mass of Li in the cell = 6.075/6.02 * 6.94 = 0.70 gm
mass of Lithium in Power wall = 590*0.7 = 413 gm
c)
Total lithium deposits in the world are estimated at 20 x 10
9
kg. One concern about
Li-ion battery technology is the diminishing and finite amount of the lithium resource; it
is estimated that all the lithium in the world could only electrify 62% of the world’s
vehicle fleet. If 500 million homes were to install a first-generation Powerwall, what
percentage of the world’s lithium resources would be used up?
[5 points]
Total Lithium deposits = 20.0E+9 kg
Li per Powerwall battery = 413 gm
Total lithium required for 500M batteries = 500E+6 *413 gms
= 2.065E+8 kg
% of Lithium used up = 2.065E+8/20.0E+9 = 1.03 %
d)
Review the following discharge curves for a lithium coin battery (the type commonly
found in watches). The battery has a rated capacity of 240 mAh and a voltage cutoff of
1.6 V, below which the voltage is too low to power the device. Estimate the difference in
energy delivered when the rate of discharge is 3.0 mA vs. 0.5 mA. Your estimates can be
very rough – one significant figure – so long as they are grounded in the basic
characteristics of the discharge curves. What explains the difference? [10 points GRAD
ONLY]
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3)
The Net Zero America [25 points for undergrad, 40 points for grad]:
The Net Zero America project, developed by a group of researchers at Princeton
University, lays out five potential pathways to decarbonizing the U.S. economy by
2050. Modeling methodology and results can be found at
https://netzeroamerica.princeton.edu
. Use this site to answer the following
questions.
a)
In a few sentences, explain why we discuss climate change in a course like
Energy and Society. What is the relationship between energy and climate change?
What is the relationship between climate change and society? List the six pillars
of decarbonization. [3 points]
Fossil fuel consumption results in CO2 emissions, and energy-related CO2 emissions
are a major portion of GHG emissions.
Climate change has very serious implications on the societal well-being. For
example, extreme weathers have been causing huge economic losses to affected
localities.
b)
List the five pathways for decarbonization. What are the major similarities and
differences between these pathways? Include at least three similarities and three
differences. [2 points]
· highly electrified demand, relatively unconstrainted supply side
· less highly electrified demand, relatively unconstrainted supply side
· less highly electrified demand, high biomass supply
· highly electrified demand, constrained renewable supply
· highly electrified demand, 100% renewable supply
similarities: amount of demand, technology prices and efficiencies, fuel costs
differences: rate of electrification, max growth rate of renewables, availability of biomass
and CCS
c)
For the following parts, use data from the reference scenario in 2050 and the
highly electrified demand/100% renewable supply scenario in 2050.
i)
Efficiency: What is the percent change in final energy use and total
emissions between the reference and decarbonized scenarios? What would
explain the change in final energy use and total emissions respectively? [5
points]
REF final energy use: 77254 PJ E+RE+ final energy use: 52029 PJ (52029-77254)/
77254*100=-32.6%
REF total emissions: 4.46187 Gt CO2 E+RE+ total emissions: -0.26618 Gt CO2
(-0.26618-4.46187)/ 4.46187*100=-106.%
ii)
Electrification: What fraction of total energy use is met by electricity in
the reference and decarbonized scenarios? Break this down by end use
sector (transportation, residential buildings, commercial buildings, and
industry) for each scenario. What would explain the variation between
sectors? [5 points]
REF final energy use: 77254 PJ
REF final electricity use: 17662.87325 PJ 17662/77254*100=22.9%
REF transport energy use: 25678.6765 PJ REF transport electricity use: 526.42236 PJ
526.4/25678.7*100=2.05%
REF residential energy use: 10786.61365 PJ REF residential electricity use:
6172422.921 TJ 6172422.9/(10786.6*10^3) *100=57.22%
REF commercial energy use: 9954.63838 PJ REF commercial electricity use:
5965235.292 TJ 5965235.3/(9954.6*10^3) *100=59.92%
REF industry energy use: 30834.51769 PJ REF industry electricity use: 4998792.683
TJ 4998792.7/(30834.5*10^3) *100=16.21%
E+RE+ final energy use: 52029 PJ
E+RE+ final electricity use: 25202.46492 PJ 25202.5/52029*100=48.44%
E+RE+ transport energy use: 13648.81241 PJ E+RE+ transport electricity use:
6900.1365 PJ 6900.1/13648.8*100=50.55%
E+RE+ residential energy use: 6512.28389 PJ E+RE+ residential electricity use:
5697184.848 TJ 5697184.8/(6512.3*10^3) *100=87.48%
E+RE+ commercial energy use: 7296.94003 PJ E+RE+ commercial electricity use:
6589897.571 TJ 6589897.6/(7296.9*10^3) *100=90.31%
E+RE+ industry energy use: 24571.75609 PJ E+RE+ industry electricity use:
6015245.995 TJ 6015246/(24571.8*10^3) *100=24.48%
Industry (8.27% change), residential (30.26% change), commercial (30.39% change),
transportation (48.5% change)
iii)
Clean Electricity: For both the reference and decarbonized scenario, what
percent of total electricity generation comes from renewable sources
(solar, wind, hydro, geothermal, biomass)? What would be the advantages
and disadvantages of allowing for zero emission sources, such as nuclear
and carbon capture? [5 points]
REF total: 5262.042 TWh
REF renewable: 2312.745 TWh REF zero emission: 2706.990 TWh
renewable 2312.745/5262.042*100=43.95% zero emission
2706.990/5262.042*100=51.44%
E+RE+ total: 15950.531 TWh
E+RE+ renewable: 15898.309 TWh
E+RE+ zero emission: 15898.539 TWh renewable
15898.309/15950.531*100=99.67% zero emission
15898.539/15950.531*100=99.67%
iv)
Clean Fuel: What is the percent change in bioenergy and hydrogen use
between the reference and decarbonized scenarios? What are some of the
benefits and challenges associated with this change in bioenergy and
hydrogen use respectively? [2 points]
REF biomass input: 141256.541 thousand tonnes E+RE+ biomass input: 584359.037
thousand tonnes (584359.037-141256.541)/141256.541*100=313.7%
REF hydrogen output: 944.308 PJ
E+RE+ hydrogen output: 19047.655 PJ (19047.655-944.308)/
944.308*100=1917%
v)
Carbon Capture: How much carbon must be removed from the atmosphere
through carbon capture in the decarbonized scenario, expressed as a
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
percent of total emissions in the reference scenario? Where are these
remaining emissions coming from? [3 points]
REF total emissions: 4.46187 Gt CO2
E+RE+ annual carbon capture: 689.092 MMT
689.092/(4.46187*10^3)*100=15.44%
d)
A carbon tax is often considered a theoretically ideal, though politically
intractable, policy solution for reducing emissions because it forces emitting
entities to internalize the externalities associated with emitting carbon, and
therefore efficiently reduce emissions according to their abatement cost. How
might a carbon tax be insufficient for achieving any of these decarbonization
pathways? [8 points GRAD ONLY]
e)
In addition to considering economic cost and technical feasibility of
decarbonization pathways, the study also considers impacts to labor and public
health. Aside from the inherent value of these factors, why might it be important
to include them in a study of this type? [7 points GRAD ONLY]
4)
Personal Carbon Accounting [25 points]:
Former ERG PhD student Chris Jones has
created a tool for individuals to estimate all direct and indirect emissions of GHGs in
CO
2
-equivalent units resulting from their choices regarding travel, home, food, and
shopping. Go to Chris’s website
(
https://coolcalifornia.arb.ca.gov/calculator-households-individuals
) and use the
calculator to answer the following questions regarding your carbon footprint. You can
choose to provide values for just yourself or for your whole household – either is
acceptable.
a)
List your annual emissions (tons/year) for each of the categories named by the
calculator (travel, home, food, goods, and services). What is the ratio of the
highest category of your emissions to the lowest? What is the ratio of your total
emissions to the national average of roughly 22 tons of CO
2
per person per year?
What is the ratio of your total emissions to the global average of 6 tons of CO
2
per
person per year? [10 points]
Travel: 9 t/yr Home: 5.0 t/yr Food: 4.0 t/y Goods: 6.0 t/y Services: 4.0 t/y Highest:
lowest = 9/3.0 = 3 My emission to national average = 28/22 = 1.26 My emissions
to global average = 28/6 = 4.66
b)
What do you find most surprising about your results? Please explain in a short
paragraph. [5 points]
I'm surprised that my travel emissions are the highest, significantly influencing my
overall carbon footprint. This indicates the substantial impact of personal
transportation choices on greenhouse gas emissions.
c)
What lifestyle changes would you have to make in order to emit no more than the
global per capita average of 6 tons of CO
2
? To do this, change the values you
entered in the calculator until your total emissions are below 6 tons CO
2
. Try to
make realistic choices. What do the results say about how your lifestyle compares
to the lifestyles of the majority of people on the planet? Could you live at or
below the global average? Please explain in a short paragraph. [5 points]
To reduce my emissions to the global average of 6 tons CO2, I'd need to majorly cut
down on travel and optimize home energy use. This indicates a significant
lifestyle shift compared to many globally, highlighting the challenges and
potential adjustments required for a more sustainable lifestyle.
d)
There is ample critique of environmentalist movements that center personal
responsibility rather than collective action (e.g. campaigns encouraging recycling
and reusable straws). An oft-cited statistic from the 2017 Carbon Majors report
indicates that more than 70 percent of global greenhouse gas emissions are
attributable to only 100 companies. Figures on the political left argue that this
indicates an urgent need to direct policy toward penalizing polluting companies
and incentivizing innovation in emission-reduction technologies for industries.
Present three arguments each for the “personal responsibility” and “industry
regulation” frameworks of environmentalist movements. [5 points]
●
Personal Responsibility:
Empowers individuals to contribute to climate solutions.
Promotes sustainable consumer behavior.
Raises awareness about environmental issues.
●
Industry Regulation:
Targets major emission sources for a significant impact.
Enables systemic change through policy and innovation.
Holds corporations accountable for environmental harm.