The student pilot flew 1.4 hours earlier that day with his CFI, then departed on his second solo flight to practice landings. The first full-stop taxi back landing reportedly resulted in the airplane porpoising slightly. The student departed to perform another landing, which according to the operator, resulted in a bounced landing. The student reportedly applied forward elevator control input resulting in collapse of the nose landing gear, and subsequent fire which destroyed the airplane. There was no reported preimpact failure or malfunction of the airplane or its systems.