Using the charge capacity of the battery derived in c, use dimensional analysis techniques Determine the dimensions of Q using only mass, length and time. 1. 2. Determine the equation that governs charging time of the battery. If the charging current is 10 A. Find charging time assuming the values provided ir 3.
Using the charge capacity of the battery derived in c, use dimensional analysis techniques Determine the dimensions of Q using only mass, length and time. 1. 2. Determine the equation that governs charging time of the battery. If the charging current is 10 A. Find charging time assuming the values provided ir 3.
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Answer this question. Part (d).
![Task 1
The 96 prismatic lithium-ion battery cells were manufactured in Korea and the Scottish firm
Axeon assembled them into a 1411-pound, 338-volt pack that provides a 71-kWh energy
capacity and a claimed 1D miles of range [Note: replace D with your ID's last two digits].
(a)
1. What is the charge capacity of the battery?
2. What is the average current that the battery can deliver if it's used continuously for
20 hours?
3. Calculate the rate of energy consumption per meter (Joule/meter).
(b) The company is conducting set of experiments to maximize the time needed to discharge
the battery. It was found that the time (t) is proportional to different powers of
acceleration (a), mass (m), and energy (E) of the battery. Use dimensional homogeneity
to find the formula of the time and the value of overall dimensionless proportional
constant using t=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 1D
km/hr, and the mass is 14D-pound.
(c) Assume that the charge capacity of the battery can be given by the following formula:
Q = Gnm³V-21²w0.5, E2
Where m is the mass of the cell of the battery in kg. V is the voltage of the battery in volts,
lis the length of the cell in m, w is the width of the cell in m, and E is the Energy of the cell
in kWh, and n is the number of cells in the pack.
If n = 100, m = D pound, 1= 25 cm, w= 5 cm, V=338 V and E=DkWh. Find the value
1.
of dimensionless constant G?
(d) Using the charge capacity of the battery derived in c, use dimensional analysis techniques to:
1.
Determine the dimensions of Q using only mass, length and time.
Determine the equation that governs charging time of the battery.
If the charging current is 10 A. Find charging time assuming the values provided in c
are valid values for part d.
2.
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Transcribed Image Text:Task 1
The 96 prismatic lithium-ion battery cells were manufactured in Korea and the Scottish firm
Axeon assembled them into a 1411-pound, 338-volt pack that provides a 71-kWh energy
capacity and a claimed 1D miles of range [Note: replace D with your ID's last two digits].
(a)
1. What is the charge capacity of the battery?
2. What is the average current that the battery can deliver if it's used continuously for
20 hours?
3. Calculate the rate of energy consumption per meter (Joule/meter).
(b) The company is conducting set of experiments to maximize the time needed to discharge
the battery. It was found that the time (t) is proportional to different powers of
acceleration (a), mass (m), and energy (E) of the battery. Use dimensional homogeneity
to find the formula of the time and the value of overall dimensionless proportional
constant using t=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 1D
km/hr, and the mass is 14D-pound.
(c) Assume that the charge capacity of the battery can be given by the following formula:
Q = Gnm³V-21²w0.5, E2
Where m is the mass of the cell of the battery in kg. V is the voltage of the battery in volts,
lis the length of the cell in m, w is the width of the cell in m, and E is the Energy of the cell
in kWh, and n is the number of cells in the pack.
If n = 100, m = D pound, 1= 25 cm, w= 5 cm, V=338 V and E=DkWh. Find the value
1.
of dimensionless constant G?
(d) Using the charge capacity of the battery derived in c, use dimensional analysis techniques to:
1.
Determine the dimensions of Q using only mass, length and time.
Determine the equation that governs charging time of the battery.
If the charging current is 10 A. Find charging time assuming the values provided in c
are valid values for part d.
2.
3.
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