This nerd sniped me and I had to do the math to confirm, but you're right, at least depending on where you get your estimates and regional power costs. The energy equivalent between a cell phone and shower time is on the order of seconds.
My phone's battery is 4385 mAh @3.7V, or 0.016 kWh, and my power costs $0.1252/kWh, or about $0.002 per phone charge. Based on some super surface-level estimates from googling, a typical shower is about 2 gallon/min, and the cost to heat water is about $0.01-0.02 per gallon, meaning for me it's actually about 4 seconds of hot water per phone charge.
And the parent comment said “47% wasted power … extra second … would offset half of that” and 47% of four seconds is about two, half of that is one second, so I’d say that was shockingly accurate, wow!
Yeah, the math I did was for heating water by 50 kelvins for a 9 l/min showerhead, which in hindsight was probably overestimating it. It'd make sense if the actual answer for most people was 2-4 seconds
My phone's battery is 4385 mAh @3.7V, or 0.016 kWh, and my power costs $0.1252/kWh, or about $0.002 per phone charge. Based on some super surface-level estimates from googling, a typical shower is about 2 gallon/min, and the cost to heat water is about $0.01-0.02 per gallon, meaning for me it's actually about 4 seconds of hot water per phone charge.