This law is often called the conservation of energy law and, this is essentially true. This law is typically either stated for a system (control mass) undergoing a cycle and then for a change of state of a system.
The first law relates two forms of energy—heat and work—of an object. For example, when a car engine has transferred some work to a car, the car's speed is increased, so the kinetic energy increase can be related to work. Also, if a stove provides a certain amount of heat transfer to a pot with water, the water temperature increase can be related to the heat transfer. More complicated processes can also occur, such as the expansion of very hot gases in a piston cylinder, as in a car engine, in which work is given out and at the same time heat is transferred to the colder walls. Other applications may be observed in which a change in state occurs without any work or heat transfer, such as a falling object that changes kinetic energy at the same time it is changing elevation.
A control mass may undergo a cycle, where it goes through a number of processes and comes back to the same state that it began at. Also, a part of the cycle may be examined, which would involve a change in state by undergoing a process. Therefore, the first law may be examined with respect to the whole cycle, which would involve a fairly simple mathematical examination, or the first law may be examined with respect to a selected part of the cycle.