Congress approved and sent to President Carter yesterday the emergency natural gas bill which supporters hope will help ease the fuel shortage in the frigid northeast and midwestern states.

This first major piece of legislation sent to the new President - and just before his first "fireside chat" to the nation - won final Senate approval by voice and House approval 336 to 82 after minor differences between their two versions were settled.

The bill empowers the President to declare a natural gas emergency and then take two temporary actions. He could, until April 30 when the cold weather is expected to be over, order interstate gas pipelines to switch gas from surplus to shortage areas. And he could, until July 31, waive controls on the price interstate pipelines may pay producers for natural gas and permit them to pay any "just" price in an effort to get more gas into their pipelines flowing north.

Gas provided by these actions could be used only to heat homes, hospitals, small businesses and other establishments where loss of heat would endanger health or destroy property. It could not be used to reopen factories closed by the cold.

No one seemed to know during the hearings and debates in Congress how much gas the bill might provide to distressed areas. The general feeling was that it wouldn't add much but that it might prevent cutting off gas from homes in some areas and this was worth doing.

Members who have tried in vain for more than 20 years to decontrol the price of interstate natural gas argued that the only way to get more gas out of the ground and assure against future shortages is to enact a permanent decontrol bill.

Ben Clarence J. Brown of Ohio, Republican manager of the bill and longtime supporter of decontrol, said the bill "will protect homeowners and is worthy of passage." But he added that "it will provide no gas for industry. It will not open any closed plants. Nor does it do anything for next winter."

Carter plans to send to Congress a comprehensive energy program in April. During the presidential campaign he said he favored deregulation of natural gas.

The price of natural gas piped across state lines is regulated by the Federal Power Commission and now sells for $1.44 per thousand cubic feet.

Gas consumed within the state where it is produced, such as Texas and Louisiana, is not regulated and sells at about $2 per thousand cubic feet in Texas. It is this intrastate gas that the pipelines would try to buy when price controls are temporarily removed.