The total energy possessed by all the particles of a gas is called the internal energy of the gas, U.

If work is done, the internal energy can be changed.

If the gas is in an insulating container, the change in internal energy is equal to the work done

If the gas is in a conducting container then energy, Q, can enter or leave the gas. If no work is done

The process of changing the internal energy of a gas without doing work is called heating^* (or cooling) the gas.

Combining the two statements gives the first law of thermodynamics, usually stated as

This law is a thermodynamic statement of the law of conservation of energy.

A useful form of the equation is

If Q entering the gas is positive.
Work done on the gas is positive.