Expansion work of a gas

We now consider the work involved in expansion and compression of the gas in the cylinder-and-piston device of Fig. 3.4. This kind of deformation work, for both expansion and compression, is called expansion work or pressure-volume work. 

Keep in mind that the system is just the gas. The only moving portion of the boundary of this system is at the inner surface of the piston, and this motion is in the -fx or —x direction. The X component of the force exerted by the system on the surroundings at this portion of 

It will be convenient to change the work eoordinate from x to V. The gas volume is given by F = A x so that an infinitesimal ehange dx ehanges the volume by dV = A dx. The infinitesimal quantity of work for an infinitesimal volume change is then given by 

During expansion (positive dV), die is negative and the system does work on the surroundings. During compression (negative dV), die is positive and the surroundings do work on the system. 

When carrying out dimensional analysis, you will find it helpful to remember that the product of two quantities with dimensions of pressure and volume (such as dV) has dimensions of energy, and that 1 Pa m is equal to 1J. 

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