The total charge a battery can supply is rated in mA·hr, the product of the curr

Question

The total charge a battery can supply is rated in mA·hr, the product of the current (in mA) and the time (in hr) that the battery can provide this current. A battery rated at 1000 mA·hr can supply a current of 1000 mA for 1.0 hr, 500 mA for 2.0 hr, and so on. A typical AA rechargeable battery has a voltage of 1.20 V and a rating of 1800 mA·hr.

How much time is required for this wire to raise the temperature of 25.0 g of water from 23.0 °C to 50.0 °C? The wire is completely submerged in the water and all the energy dissipated in the wire is absorbed by the water. (Answer: 1.09 hours)

Explanation / Answer

specific heat of water

4186 J /kg-K

to raise the temp of 25 g of water from 23 to 50 deg C energy requred

                     = 4186 *0.025*(50-23) = 2825.5 J

Battery rating   1.2 V , 1800mA-hr

if we draw current at 1.8 A, energy decipated is

1.2*1.8 = 2.16 J /s

2825.5/2.16 = 1308 s

The current is not specified, time depends on the current at which we re drawign power from battery.

If we use 500 mA current then

power = 1.2 *0.5 = 0.6 J/s

then time = 2825.5/0.6 = 4709 s = 1.31 hrs

for the given answer it looks like current I = 0.6 A, not given then

power 1.2*0.6 = 0.72 J/s

then time t = 2825.5 /0.72 s = 1.09 hrs

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