12 INTRODUCTION. CHAP.
Work done by Change of Volume. — If we have of a substance in the liquid condition contained in a vessel of section, then its height in the vessel will be (Fig. 2). On the surface of the liquid let there rest a weighted piston, so that there is a pressure of 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 .
In order that this expansion may take place, the weighted piston resting on the sur- face must be raised through , whereby the work will be done.
From this it is clear that when any substance whatever expands by the work done is if the pressure is expressed in dynes per square centimetre.
In Fig. 3 the shaded portion represents the original volume of a substance, whilst the outer contour represents the volume after expansion. Let us consider the small element of surface . This has been displaced through , and the work done by it is , since there is a pressure on , If we denote the volume . by , then the work is ; and if we calculate for the whole substance we must take the sum of all the products, . Since now possesses the same value for all parts of the surface, and as the sum of all the volumes is evidently equal to the total change of volume , the total work done will be (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
