A lithium ion battery bank is being charged over a period of two hours, during which it consumes 10
kWh of electrical energy. During
this time, its temperature increases from ambient (25 °C) to 50 °C and
is retained at 50 °C until the end of the charging process. Also, the battery loses Otosa = 3 MJ of heat
during this charging process. If the mass of the battery is m= 100 kg, and the battery could be considered
a solid for sensible energy purposes with a heat capacity c = 3,000 J/kg-K. While answering the
questions below, carefully indicate the system under consideration and write the first law for this
system.
The change in sensible energy of an incompressible solid can be computed from AU sensible = mc 47
(5 marks) What is the total change in internal energy Au, and what is the change in internal
energy associated with chemical bonds AUchemical inside this battery during the charging period? How
would you define the efficiency n of the charging process and what is the value of this efficiency for
this battery during the above-mentioned charging process? State your answer after careful depiction
b. (5 marks) The same (charged) battery is now allowed to cool to ambient temperature. After it
cools, it is discharged over a period of 3 hours during which it loses loss = 2 MJ of heat to the ambient
and gets heated to 40 °C. At the end of the discharge period, the battery is once again allowed to cool
down to ambient temperature. At the end of the cool-down period, the battery is restored to its original
state (the state before the charging process). How much electricity did the battery generate (in kWh)
while discharging? How would you define and calculate the round-trip efficiency of this battery?
Round-trip, efficiencies are critical to energy storage applications and are related to the energy lost
during charge-discharge cycles.
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