Years ago - pre-POTA and pre-lithium - some intrepid QRPer (a W3-lander) decided to see how many states he could work with a single 9V alkaline battery during Sweepstakes. I don't remember his results but his radio was a new-at-the time Norcal 40A.
These days, any weekend POTA activation can serve as a test platform for this and other absurdities.
I decided to see if a 9V alkaline battery could power my TR-35 long enough to make the 10 contacts required for a valid POTA activation. The TR-35 draws 90-100 mA on receive. Transmit current (with 9V DC in) is 700mA and that results in an RF output of about 1 watt on 20m and 2.5 watts on 40m.