Immersion heaters like the one pictured are typically plugged in. I'm interested in potentially developing one that is battery operated so it can be used on backcountry camping trips. A water heating calculator (https://www.easycalculation.com/physics/thermodynamics/water-boiling-time-calculator.php) informed me that 500W will bring half a liter of 20°C water to 70°C in 4 minutes assuming 80% efficiency.
My question is: what size battery would be required to deliver 500W for 4 minutes say 20 times before requiring recharge? Would it be small/light enough to be practical to carry on an extended hike?