
This new battery charges to 70% in two minutes, and lasts for 20 years - nreece
http://www.sciencealert.com.au/news/20141410-26327.html
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thecabinet
A fun game to play with any new battery charging press release is to figure
out how hot the thing will be after charging.

An iPhone 5 has a 5.45 Wh battery, which is approximately 20kJ. 70% of that is
14kJ. Charging a lithium-ion battery is typically 80-90% efficient, so getting
14kJ of energy into the battery will also put approximately 2500J of heat into
the handset. It takes just shy of 4J to raise 1g of water by 1°C, but that
iPhone has a density (112g / 55ml) about twice that of water, so it will be
about 2.7°C (5°F) hotter than before you started charging.

I think.

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kale
You were right up until density. The amount of energy it takes to raise the
temperature by one degree Celcius, per gram of the material is the specific
heat capacity. Theoretically, it could have a lower specific heat capacity
than water despite being twice as dense (I doubt it though).

In addition, using that analysis assumes that the phone is in a vacuum, or is
somewhere were it is not getting rid of heat through convection, conduction,
or radiation.

In steady state temperature analysis, you have the rate of heat going into the
phone, and the rate of heat being conducted away from the phone over the
surface area. Say, 10W in (5V at 2A) is the rate of charge, and 1W will be
converted to heat. The phone gets rid of heat at a rate that is proportional
to its temperature. A phone 10 degrees warmer than the surrounding air will
release more heat into the air than a phone 3 degrees warmer.

In a steady state analysis for our example(which 2 minutes may not be
appropriate for!), let's say the phone gets rid of 0.5W of heat at 1 degree
above room temp, 1W at 2 degrees above room temp, and 2W at 4 degrees above
room temp. If the rate of heat going into the phone is 1W, then the phone will
eventually become 2 degrees warmer than the surrounding air to reject that
heat.

I made up these numbers as an example of how you would discover how hot the
phone would get. You'd need a calorimeter to submerge the phone in to measure
a lot of this stuff.

