MD Problem Set 7
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C100
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English
Date
Feb 20, 2024
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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]
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