Battery manufacturers are constantly pushing technology development towards higher

specific energy density $($i$.$e$.$ Wh$/$kg or MJ$/$kg$).$ You are asked to calculate how much the

mass of non$-$active components $($e$.$g$.,$ current collector, binder, plastic, etc.$)$ would need to

be reduced to further enhance specific energy density.

Consider a lithium ion battery with anode and cathode capacities of CA$=350$ mAh$/$g;

CC$=150$ mAh$/$g$,$ respectively, and a cell potential of $4$V$.$

The practical specific energy density of this battery is $140$ mWh$/$g$.$

Management is pushing for a performance improvement to achieve a next$-$generation

battery with a specific energy density target of $250$ mWh$/$g$.$

$($a$)$ By how much would the mass of inactive components need to be reduced to meet

this target?

$($b$)$ What would be some practical implications of reducing the mass of inactive

components $($i$.$e$.,$ thinner electrodes, thinner separator, less binder$)?$