1. The problem statement, all variables and given/known data 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. 2. Relevant equations The first law of thermodynamics ΔE = Q -W 3. 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 and Q21 = -584kJ the answer in the book is +440kJ. Why? What have I done wrong?