Page:Text-book of Electrochemistry.djvu/29

12 INTRODUCTION. CHAP. Work done by Change of Volume. — If we have $$v c.c.$$ of a substance in the liquid condition contained in a vessel of $$1 sq. cm.$$ section, then its height in the vessel will be $$v cm.$$ (Fig. 2). On the surface of the liquid let there rest a weighted piston, so that there is a pressure of $$P dynes$$ opposing the expansion of the liquid.

If the liquid be now warmed, or if a chemical reaction take place in it, then the volume changes; let the change be represented by an expansion of $$dv c.c$$.

In order that this expansion may take place, the weighted piston resting on the sur- face must be raised through $$dv cm.$$, whereby the work $$Pdv$$ will be done.

From this it is clear that when any substance whatever expands by $$dv c.c.$$ the work done is $$Pdv ergs$$ if the pressure $$P$$ is expressed in dynes per square centimetre.

In Fig. 3 the shaded portion $$K$$ represents the original volume of a substance, whilst the outer contour represents the volume after expansion. Let us consider the small element of surface $$dA sq. cm$$. This has been displaced through $$h cm.$$, and the work done by it is $$P.dA.h ergs$$, since there is a pressure $$P.dA$$ on $$dA$$, If we denote the volume $$h$$. $$dA$$ by $$dw$$, then the work is $$P. dw ergs$$; and if we calculate for the whole substance we must take the sum of all the products, $$P. dw$$. Since now $$P$$ possesses the same value for all parts of the surface, and as the sum of all the volumes $$dw$$ is evidently equal to the total change of volume $$dv$$, the total work done will be $$P.dv ergs$$ (as given above).

Work done by Evolution of a Gas under Constant Pressure. — We can now calculate the work done when a gas is formed at constant pressure; for instance, by the boiling of water. For the sake of simplicity, let us take a gram-molecule (18 grams) of water vaporising at a pressure of