Why the first law is not enough
The first law accounts for conservation of energy, but conservation alone does not describe which thermal processes are possible. A heat engine cannot operate by taking energy from one thermal reservoir and converting all of it into mechanical work.
The second law of thermodynamics requires a heat engine to operate between a hot source and a colder sink.
Some of the energy transferred from the source can become useful work, but the remainder must be transferred to the colder sink.
Here, is the energy transferred from the hot source, is the work output and is the energy transferred to the cold sink.
Direction of thermal transfer
Thermal energy transfers naturally from a region at higher temperature to one at lower temperature. It does not spontaneously pass from a colder region to a hotter one.
If the working substance of an engine reached the same temperature as its hot source, there would be no temperature difference to drive further thermal transfer from that source. The engine could therefore no longer continue to obtain work in that way.
Exam Tip: When stating the second law for a heat engine, include both reservoirs: the engine must operate between a source and a sink, and some energy must be rejected to the colder sink.