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1.6.2 The Work
Work is energy in transition between a system and its surroundings by virtue of a
force. Work is done by a system on its surroundings if the sole external effect of the
interaction could be the lifting of a body. The magnitude of work is the product of the
weight of the body lifted and the distance it would be lifted if the lifting of the body
were the sole external effect of the interaction. This definition points out that work
involves both a system and something outside the system, whether it is called the
surroundings or another system. In two systems A and B, interacting only with each
other, the work done by system A is work done on system B and vice versa. The
definition tells how to identify and measure the work done system. Work done on a
system must be identified as work done by some other system.
Consider a system comprised of a compressed coil spring. As the spring expands
against some part of its surroundings, the action of the spring on its surroundings could
be reduced to the lifting of a weight. It does not matter whether the spring is actually
being used to move an object against frictional resistance, to accelerate a body, or to
push a plunger that in turn forces a fluid to flow through a small opening. The important
fact is that the sole external effect could be the lifting of a weight while the spring
undergoes the same process.
Consider a system that is a gas trapped in a cylinder behind a movable piston. If the
gas expands, pushing the piston outward, the sole effect external to the gas could be the
lifting of a body. If frictional effects are present in the surroundings, there may actually
be effects other than the lifting of a body. For example, the temperature of some part of
the surroundings may increase. However, if the frictional effects are reduced, the
limiting case in which the sole external effect is the lifting of a weight is approached.
The limiting condition of no friction in the surroundings is a useful concept in the
identification and measurement of work. The use of this concept does not restrict us to
the consideration of processes that involve no friction. It must be remembered that in
deciding whether a certain interaction of a system with its surroundings is work, we ask,
not if the sole external effect is the lifting of a weight, but rather: "Could the sole
external effect be the lifting of a weight?" In seeking an answer to this question we
consider as one possibility the limiting case of no friction in the surroundings.

1.6.3 Calculation of the Work
Let us consider a gas enclosed in a cylinder, as shown in fig.7. Let the volume of
the gas be V and pressure be p. If the area of the piston is S, the force exerted by the
gas on the piston will be pS, since p denotes pressure or force per unit area. Suppose
the gas pushes the piston outwards through a small distance dx. When a force multiply
of a distance, which is why a work done by the gas on the piston is:

dL  pSxdx  P (Sdx ) (1.25)

But Sdx is the small increase in the volume of the gas. If we denote it by dV, then:

dL  pdV (1.26)

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