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How long will a Xantrex X Power pack 1500 supply electricity and can a industrial hairdryer function from it?

I want to start a mobile groomer and need a powersupply that is quiet. Thanks guys you were both a great help.

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1. 1500 means the amount of wattage that the inverter puts out. That is about 11 amps, if your dryer draws less than 11 amps. The inverter will power the dryer. The problem is an inverter ups the voltage from 12 volts DC to 120 volts AC. Which means you need a lot more amps than 11 to up the voltage. 10 times if there was no losses. That would be 110 amps. With the losses, it probley would to 200 amps. I use a 500 watt inverter for 120 volts for the tv on my boat. Which doesn't draw much current, (amps). You would be better off looking into a real quiet generator. They are out there, Honda makes a real quiet 2000 watt generator. Or less efficient a engine driven generator like that a carpet cleaner mobile van uses.
2. You are pushing it. Many hair dryers use anywhere from 2000 to 2500 watts. An overload with your inverter. How long is a function of total draw and the ampacity of your batteries. Either step up your inverter capacity or look at a Onan Whisperlite.