Thermodynamics is the study of the flow and transformation of energy. Historically, thermodynamics was developed to understand how to make steam engines more efficient. Therefore, a distinction was made between the two forms of energy, heat and work, and the central question to be addressed was how to transform a larger fraction of heat into work.
Heat (Q): The energy that flows across the boundary of a system due to a temperature difference between the system and the surroundings. This difference can be infinitesimally small.
Work (W): The energy that flows across the boundary of a system that is not heat. Examples include mechanical energy and electrical energy.
Definition Of Sign Convention
Since heat Q and work W are signed scalar quantities, we must be consistent in the use of the signs. We shall use the convention that energy input to the system is looked as positive quantity.
In thermodynamics, the system is where the energy transformation we are interested in takes place. The system is separated from its environment (or surroundings) by a boundary. The systems we are going to study extensively are pistons and engines. The boundary may be real or imaginary, fixed or moving. We are interested in the Q and W that cross this boundary.
To make the algebraic sign convention clear:
Q is the heat input into the system and -Q is the heat output from the system; W is the work input into (work done on) the system and -W is the work output by (work done by) the system.
Thus Q ≡ Qin and -Q ≡ Qout; W ≡ Win and -W ≡ Wout.
Further notation: We will later for convenience also use Qh to denote heat input into the system from a hot reservoir, and Qc to denote heat output from the system to a cold reservoir when we study heat engines. Therefore Qh ≡ Qin and Qc ≡ Qout. We will use whichever notation is the most convenient.