Battery efficiency and internal energy

[spyboy]

Homework Statement

One rechargeable battery of mass 15.0 g delivers to a CD player an average current of 15.5 mA at 1.00 V for 2.50 hr before the battery needs to be recharged. The recharger maintains a potential difference of 2.00 V across the battery and delivers a charging current of 10.0 mA for 4.90 hr.
a.) What is the efficiency of the battery as an energy storage device? There will be no units for efficiency. (Hint: Efficiency is the ratio of energy used by the CD player to the energy delivered by the charger.)
b.) How much internal energy is produced in the battery during one charge-discharge cycle?

Homework Equations

E=I*V*t
Efficiency = Eout/Ein

The Attempt at a Solution

I got part a easily enough (.395), but part b has me stumped. Initially, I thought that internal energy loss would be the difference between Eout and Ein (Ein-Eout). Eout I got to be .03875 J, and Ein is .098 J. The difference between them is .05925, but this isn't the correct answer. Any suggestions?

 

[anathema]

For part b, you are correct in thinking that the internal energy loss is the difference between Eout and Ein. However, you need to consider the charging and discharging separately.

During the discharge, the battery delivers an average current of 15.5 mA at 1.00 V for 2.50 hr, so the energy used by the CD player is:

Eout = (15.5 mA)(1.00 V)(2.50 hr) = 0.03875 J

During the charging, the battery receives a current of 10.0 mA at 2.00 V for 4.90 hr, so the energy delivered by the charger is:

Ein = (10.0 mA)(2.00 V)(4.90 hr) = 0.098 J

The internal energy produced during one charge-discharge cycle is then:

Einternal = Ein - Eout = 0.098 J - 0.03875 J = 0.05925 J

Hope this helps!