Industrial production rose sharply for the second consecutive month in December, further evidence that the long pause in economic recovery is over.

The Federal Reserve Board reported that the output of the nation's factories, mines and utilities rose 0.7 per cent in December, after a 1.2 per cent advance in November. About half the strong November rise was because of a rebound from the Ford Motor Co. strike in September and October.

John W. Kendrick, chief economist for the Department of Commerce, said industrial production, which increased at an annual rate of 8.4 per cent in December, is "getting up toward" the range needed to meet President-elect Carter's total growth goal of 6 per cent.

The morning the Commerce Department will announce the growth of all goods and services produced during the final three months of last year. Government economists say that so-called real gross national product will grow more slowly than the 3.9 per cent annual rate registered in the third quarter.

But the economy was picking up steam later in the quarter.

Industrial production, for example, an important part of overall gross national product, fell in October but grew smartly in the final months of the quarter.

In part a reflection of the rebound in industrial production, the nation's unemployment rate fell from 8.1 per cent to 7.9 per cent in December. In both months there was a big increase in the number of persons finding jobs.

The Federal Reserve said that about a third of the increase in industrial output was due to increased output of motor vehicles. The rest was spread widely among consumer and business goods with the exception of metals such as steel and aluminum.

Over the year, the central bank said, output of factories, mines and utilities increased 6.8 per cent, with most of it occurring in the first six months in 1976.

During December the output of consumer goods rose 4.5 per cent, "reflecting a 14 per cent jump in auto and utility vehicle production." Automobiles were assembled at an annual rate of 10 million "as companies sought to replenish and build stocks - particularly of the faster-selling intermediate and full-size models," the Federal Reserve said.

The agency also cited increases of 0.6 per cent in home goods such as appliances, carpeting and furniture and a 0.4 per cent increase in nondurable consumer goods such as clothing.

Business equipment rose 1 per cent in December but productionof materials, such as steel, was unchanged.