Pan American World Airways cut its losses in half to $56.2 million for the second quarter of 1982 compared with $112 million in the second quarter a year ago.

The airline also reported today that it cut its operating loss for the quarter to $41.2 million from $78 million in the year-earlier period.

Trans World Corp., parent company of Trans World Airlines, reported a $41.6 million gain today, while American Airlines recorded a slight profit.

In a presentation to industry analysts today, Pan Am Chairman C. Edward Acker called the results "a significant improvement" and promised that the airline would report a profit in the current quarter. Last year, Pan Am reported a $45 million operating loss in the third quarter; its $281.5 million net profit came as a result of the sale of its hotel subsidiary.

Acker, attracted from Air Florida last fall by the challenge of trying to turn Pan Am around, attributed the improved results to continuing gains in passenger revenue yield--the average amount of revenue received per passenger mile--combined with significant expense reductions resulting from its continuing cost-cutting efforts.

As a consequence of those factors, Pan Am's break-even load factor--the number of seats it needs to fill before it starts making money--fell from 72 percent during last year's second quarter to 62.6 percent this year, Acker told the New York Society of Airline Analysts. "In June, our break-even seat factor fell below 60 percent, and we recorded our first net profit in 22 months," he said.

Although passenger revenue from scheduled service was down 3.2 percent in the March-June period, it was offset by a 51 percent increase in revenue from charter services and an 8 percent increase in revenue from its profitable contract services.

In a continuing attempt to restructure the airline, Acker told the analysts that Pan Am will sell its 12 Lockheed L1011s and continue to reduce its fleet of Boeing 727-100s. The move will save in operating expenses by cutting the number of different kinds of airplanes being flown and by increasing use of the remaining aircraft.

Although Pan Am intends to add some routes this fall and winter--primarily from the Northeast to Florida and the Caribbean--it also plans to eliminate some long-haul, low-density routes, Acker said. Overall, the strategy will reduce Pan Am's available seat miles by about 10 percent, he said. But the routes being considered for elimination operate at load factors under 40 percent, he said.

Meanwhile, American Airlines today reported net earnings of $466,000 in the second quarter, far below the $27.8 million in the same period of 1981. After a provision for payment of preferred dividends, the company posted a loss of nine cents a common share. In the second quarter of 1981 American had earnings of 82 cents a share.

American said second-quarter revenues declined 1 percent to $1.041 billion from $1.051 billion in the same 1981 quarter, although traffic increased 10.7 percent.

In the first half of this year, American lost $41.2 million compared with net earnings of $31.7 million in the same period in 1981.

Trans World Corp. reported a 27 percent decline in second-quarter profits and a $61 million loss for the first half of the year. Net earnings fell to $41.6 million ($1.65 a share) in the second quarter from $57 million ($2.44) during the same 1981 quarter. Revenues fell 5.8 percent to $1.33 billion from $1.413 billion.

For the six months, Trans World's loss of $61 million compared with a loss of $465,000 in the same 1981 period. Revenues dipped to $2.4 billion from $2.56 billion.

The airline recorded a second-quarter pretax profit of $25.6 million and a first-half pretax loss of $84.7 million.