An automobile battery that is originally fully charged gradually discharges while sitting on a shelf at a constant temperature of 40C, producing no electric work but resulting in a heat transfer of 1000kJ to its enviroment.
The battery is then recharged to its initial state by means of a process involving work input of 440Wh.
Find the heat interaction of the battery during this charging process. Justify your answer thermodynamically.
The first law of thermodynamics
ΔE = Q -W
The Attempt at a Solution
in the first step, heat is moving out of the system and no work is done, so:
Q12 = -1000kJ
W12 = 0
in the charging process, the is done on the system, so:
W21 = -440Wh = -440[Wh]*3.6[kJ/Wh] = -1584kJ
The battery is charged to its initial state, so:
ΔE = 0
ΔE12 + ΔE21 = 0
(Q12 - W12) + (Q21 - W21) = 0
-1000kJ + Q21 +1584kJ = 0
Q21 = -584kJ
the answer in the book is +440kJ. Why? What have I done wrong?