A C180 PILOT RAN OUT OF FUEL AND LANDED IN A FIELD WHEN THE FBO FAILED TO INSTALL THE FUEL CAP.

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VFR FLT FROM ZZZ TO ZZZ1 WITH AN ENRTE FUEL STOP AT ZZZ2. FLT FOLLOWING WAS UTILIZED. DEPARTED ZZZ WITH FULL FUEL TANKS (55 GALS) AND FLEW 3.7 HRS TO ZZZ2. BURN WAS 11.5 GPH. FUEL USED WAS 42.5 GALS. AT ZZZ2 ORDERED 7 GALS PER SIDE FOR 14 GALS TOTAL AND ADDED 1 QUART OF OIL; WHICH I DID MYSELF. I SAW THE LINE BOY CLOSE THE L FUEL DOOR AS I WAS ON A LADDER FINISHING UP ADDING A QUART OF OIL IN THE ENG. WHEN THE LINE BOY WAS FUELING THE R SIDE HE WAS TALKING WITH ANOTHER COLLEAGUE ABOUT MOVING SOME OTHER ACFT SOON AND ABOUT OTHER DUTIES THEY WERE SUPPOSED TO BE DOING SOON. THE LINE BOY THEN PLACED THE FUELING LADDER ON HIS TRUCK AND DROVE OFF; WE WENT INSIDE; PAID OUR BILL AND DEPARTED. DEPARTED ZZZ2 FOR ZZZ1 WITH 26.5 GALS (12.5 GALS ON ARR IN ZZZ2 PLUS 14 GALS ADDED GAVE US 26.5 GALS) AND THE FLT TIME FROM ZZZ2 TO ZZZ1 IS 1:10 TO 1:15 ENRTE. AT 1:05 ENRTE APPROX 2-3 NM FROM THE ZZZ1 ARPT THE ENG STOPPED RUNNING; FUEL INDICATORS (FLOAT TYPE) SHOWED EMPTY ON THE L TANK BUT 1/2 OR BETTER IN THE R TANK. MONITORING FUEL GAUGES ENRTE SHOWED MORE FUEL BURNING FROM THE L SIDE THAN FROM THE R. ON CESSNAS THAT I HAVE FLOWN THIS IS NOT AN UNUSUAL SITUATION AS THEY GRAVITY FEED AND USUALLY NOT EQUALLY; SO I WAS NOT ALARMED WHEN THE L TANK APPEARED TO BE DRAINING MORE RAPIDLY THAN THE R TANK. FUEL SELECTOR WAS ON BOTH (STANDARD PROC). WHEN ENG QUIT RUNNING MY PAX SAID THAT I SAID 'I WONDER IF THAT LINE BOY PUT THE DAMN CAPS ON.' I DO NOT REMEMBER SAYING THAT AS I WAS QUITE BUSY AT THAT TIME AND PROBABLY SUFFERED A MILD CONCUSSION AFTER WE STOPPED. AT ABOUT 2000-2300 FT MSL (1000-1300 FT AGL) THE ENG QUIT. I SET UP AN 80 MPH GLIDE AND CHKED THE FUEL SELECTOR (BOTH); MIXTURE TO BE RICH (WHICH IT WAS); MAGNETOS ON; THEN SELECTED R FUEL TANK AS IT WAS SHOWING THE MUST FUEL (APPROX 1/2); NO HELP; ROCKED THE WINGS TO SEE IF I COULD GET ANY FUEL OUT OF THAT TANK; NO HELP; THEN SELECTED THE L TANK; ROCKED WINGS AGAIN; NO HELP THEN SELECTED BOTH ON THE FUEL SELECTOR; TRIED DIFFERENT MIXTURE SETTINGS WITH NO HELP AND ATTEMPTED DIFFERENT THROTTLE SETTING TO NO AVAIL. LOWERED FULL FLAPS AND BANKED L TO AVOID SOME TREES IN THE FIELD I HAD SET UP FOR. LANDED S IN A SOYBEAN FIELD. LNDG WAS OK WITH NO BOUNCE BUT THE FIELD WAS TOO SHORT AND THEN WHEN APCHING A SLIGHT RISE IN THE FIELD LEADING UP TO A 2-LANE COUNTY ROAD WE BECAME AIRBORNE OVER IT AND LANDED HARD INTO THE FIELD JUST S OF THE COUNTY ROAD APPROX 60-70 FT INTO THE FIELD. WHEN MY PAX AND I EXITED FROM OUR RESPECTIVE DOORS; WE NOTICED THE R FUEL DOOR AND FILLER CAP OPEN/OFF. THE CAP WAS CHAINED TO THE FILLER NECK SO IT WAS LAYING ON THE WING JUST AFT OF THE FILLER NECK. FUEL STAIN WAS OBVIOUS FROM THE FILLER NECK TO THE TRAILING EDGE OF THE R FLAPS; APPEARING THAT THE FUEL CAP WAS LEFT OFF BY THE LINE BOY IN ZZZ2. FUEL WAS THEN SIPHONED DUE TO THE VENTURI EFFECT OVER THE R WING. HAVING THE FUEL SELECTOR IN THE BOTH POS FURTHER EXASPERATED THE SITUATION AS THEN THE FUEL FROM THE L SIDE WAS FEEDING THE ENG BUT WAS ALSO XFEEDING THROUGH THE SELECTOR ON BOTH OVER INTO THE R TANK AND OUT THE OPENED FILLER NECK DUE TO THE VENTURI EFFECT. I BELIEVE THE FUEL FROM THE L TANK WAS EMPTIED FIRST BECAUSE AS STATED PREVIOUSLY IN THIS STATEMENT; IT WAS FEEDING THE ENG AND BEING SUCTIONED THRU THE FUEL SELECTOR ON BOTH OVER TO THE R SIDE AND OUT THE OPENED R FILLER NECK. FUEL FROM THE R TANK WAS PROBABLY FEEDING THE ENG ALSO BUT WAS RAPIDLY BEING SUCTIONED OUT THE OPENED FILLER NECK. I BELIEVE THE FLOAT TYPE GAUGE TO BE ACCURATE ON THE L TANK DUE TO THE SUCTION ON THE R TANK DRAWING FUEL FROM THE L TANK THEREBY SHOWING AN EMPTY OR NEARLY EMPTY L TANK. I THINK THE GAUGE ON THE R TANK ERRONEOUSLY SHOWED 1/2 TANK DUE TO THE SUCTION IN THAT TANK LIFTING THE FLOAT THEREBY SHOWING FUEL IN A TANK WHEN THE FUEL WAS ACTUALLY NOT THERE. LOOKING BACK AT THE SITUATION; I SUSPECT THAT THE LINE FUELER AT ZZZ2 WAS SOMEWHAT DISTR BY HIS COLLEAGUE ABOUT THE OTHER PRESSING DUTIES THEY BOTH HAD TO DO AND IT DID APPEAR THERE WAS SOME TENSION BTWN THE 2 LINEMEN.