6.3 Heat and Work

6.3 Heat and Work

We know that both heat and work correspond to transfer of energy by some means. The idea was first applied to the steam engine where it was natural to transfer heat in and get work out. Consequently, it made a sense to define both heat in and work out as positive quantities. Hence, work done by the system on its environment is considered positive while work done on the system by the environment is taken as negative. If an amount of heat $Q$ enters the system, it could manifest itself as either an increase in internal energy or as a resulting quantity of work performed by the system on the surrounding or both.

We can express the work in terms of directly measurable variables. Consider the gas enclosed in the cylinder with a moveable, frictionless piston of cross-sectional area $A$ as shown in Fig. 6.4(a). In equilibrium, the system occupies volume $V$ and exerts a pressure $P$ on the walls of the cylinder and its piston. The force $F$ exerted by the gas on the piston is $PA$.

We assume that the gas expands through $\Delta V$ very slowly, so that it remains in equilibrium as shown in Fig. 6.4(b). As the piston moves up through a small distance $\Delta y$, the work $W$ done by the gas is:

Since $A\Delta y = \Delta V$ (Change in volume)

Hence

The work done can also be calculated by area of the curve under P-V graph as shown in Fig. 6.5.

Knowing the details of the change in internal energy and the mechanical work done, we are in a position to describe the general principles which deal with heat energy and its transformation into mechanical energy. These principles are known as laws of thermodynamics.