On August 27, 2002, about 1210 eastern daylight time, a Piper PA-38-112 (Tomahawk), N4307E, was substantially damaged during a forced landing into trees, after a loss of engine power, near Athens, Ohio. The certificated student pilot was not injured. Visual meteorological conditions prevailed for the solo flight destined for Fairfield County Airport (LHQ), Lancaster, Ohio. A visual flight rules flight plan was filed for the instructional flight conducted under 14 CFR Part 91. The flight departed from Wood County Airport (PKB), Parkersburg, West Virginia, about 1150. According to the student pilot, the airplane was based at LHQ, and she had planned a round-trip cross-country flight to PKB. The fuel tanks were "topped off" the day before the accident, and after the fueling, another pilot flew the airplane. The following day, before departing LHQ, the student pilot observed that left fuel tank was full and the right fuel tank had approximately 12 gallons. The student pilot flew the airplane to PKB with the fuel selector positioned to the right tank, and landed uneventfully. The student pilot added that she did not switch tanks because she thought there was enough fuel in the right tank for the round-trip flight. During the return leg, while in cruise flight about 3,000 feet msl, the engine lost all power. The power loss occurred approximately 20 minutes after departing PKB. The student pilot did not switch fuel tanks because the right fuel gauge indicated mid-range, and she believed that adequate fuel remained in the right tank. The student pilot subsequently performed a forced landing into trees, and the airplane came to rest inverted. Examination of the wreckage by a Federal Aviation Administration (FAA) inspector revealed that the left fuel tank had remained intact, and was full of fuel. The right fuel tank had ruptured, but the inspector did not observe any evidence of fuel spill from the right tank. The right fuel tank contained about 1 gallon of fuel. The inspector further stated that the airplane was flown 1.1 hours prior to the student pilot's flight. Review of fueling records confirmed that 15.6 gallons of fuel was added on August 26. The inspector subsequently interviewed the student pilot and flight instructor. The flight instructor stated that he had met with the student pilot prior to the solo flight. He provided instruction, and entered the proper endorsements into the student's logbook. During the instruction, the flight instructor told the student pilot to fly out on the right tank, and fly back on the left tank. The student pilot confirmed the flight instructor's statement. The distance between LHQ and PKB was approximately 61 nautical miles. Review of a Piper Tomahawk Information Manual revealed that the airplane was equipped with two 16-gallon fuel tanks, and each tank held 1 gallon of unusable fuel. Further review of the manual revealed that: at best power mixture, at 75-percent power, the engine consumed 6.5 gallons of fuel per hour. Review of a discrepancies form for the accident airplane revealed that an inaccurate right fuel tank gauge was entered on July 12 and August 26, 2002. However, no corrective actions were noted.