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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, wh

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.

kale 12y ago
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.

kale 12y ago

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.