Ford Motor Co. reported second-quarter profits of $542 million yesterday and Chairman Phillip Caldwell declared the company is "on a roll."

Mobil Corp., the nation's second largest oil company, said its second-quarter profits were up 40 percent.

But Bethlehem Steel Corp., citing "unrelenting" dumping of foreign steel on U.S. markets, posted a second-quarter loss of $92.7 million, almost double its loss in the same quarter last year.

Ford's net income ($4.50 a share) is $337 million higher than the same period of 1982 and $331 million higher than the 1983 first quarter.

"I believe it would be fair to say Ford Motor Co. is on a roll," Caldwell said. "We've beat out a little clearing in the jungle and the sunshine feels good."

Ford's showing raised the combined quarterly profits of the Big Three automakers to nearly $1.9 billion. General Motors earlier reported a $1.043 billion profit, while Chrysler Corp. said it made $310.3 million.

He said if things go as well the rest of the year, employes would receive a profit-sharing payout.

Caldwell credited the improvement to further gains in Ford's car and truck business in North America, higher car industry volume, a bigger market share in Europe, and worldwide productivity improvements.

Ford's net income for the second quarter of 1982 was $204.9 million ($1.70). For the 1983 first-half, Ford made $753.4 million ($6.25), compared with a loss of $96.6 million (80 cents).

Second-quarter sales surpassed $11.7 billion, compared with $10.98 billion for the same period of 1982. For the first six months of 1983, sales totaled $21.7 billion, up from $19.8 billion in 1982.

Mobil Corp., citing stable crude-oil prices and larger profit margins on its marketing and refining operations, said its second-quarter earnings were up 40 percent.

Mobil, the nation's second-largest oil company, said profit rose to $402 million (99 cents), from $287 million (68 cents) a year earlier. Revenue fell 9 percent, however, to $14.4 billion from $15.8 billion.

For the first half of 1983, Mobil's profit gained 23 percent to $652 million ($1.61), from $531 million ($1.26) in the comparable 1982 period. Six-month revenue fell to $28.7 billion from $32.2 billion.

Mobil's Montgomery Ward unit, the nation's seventh-largest general merchandise retailer, earned $4 million--its first quarterly profit since the last quarter of 1982, when it earned $16 million, and an improvement from its $27 million loss a year earlier.

Mobil's chemical operations lost $7 million in the first half, against profit of $26 million a year earlier.

Bethlehem Steel's loss compared with a $47.1 million loss in the second quarter of 1982. It brought losses for the six months ended June 30 to $267.9 million. That compared with a loss of $113.8 million for the first six months of 1982.

Sales for the second quarter were $1.2 billion, down from $1.5 billion in the same period last year. Sales for the first six months of the year were $2.4 billion, down from $3 billion for the same period in 1982.

Donald Trautlein, Bethlehem's chairman and chief executive officer,criticized "aggressive dumping practices by foreign government-owned and subsidized steel producers who have charged extremely low prices in violation of United States trade laws." However, he said Bethlehem's second-quarter net loss was "attributable principally to continued poor customer demand in many product lines and unsatisfactory selling values."

Trautlein noted Bethlehem's loss was less in the second quarter than in the first quarter. CAPTION: Picture, Ford Motor Co. Chairman Phillip Caldwell announces profits of $542 million yesterday. UPI