In a paper communicated to the Royal Society, June 20, 1844, “On the Changes of Temperature produced by the Rarefaction and Condensation of Air,” Mr. Joule pointed out the dynamical cause of the principal phenomena, and described the experiments upon which his conclusions were founded. Subsequently Professor Thomson pointed out that the accordance discovered in that investigation between the work spent and the mechanical equivalent of the heat evolved in the compression of air may be only approximate, and in a paper communicated to the Royal Society of Edinburgh in April 1851, “On a Method of discovering experimentally the relation between the Mechanical Work spent, and the Heat produced by the compression of a Gaseous Fluid,” proposed the method of experimenting adopted in the present investigation, by means of which we have already arrived at partial results. This method consists in forcing the compressed elastic fluid through a mass of porous non-conducting material, and observing the consequent change of temperature in the elastic fluid. The porous plug was adopted instead of a single orifice, in order that the work done by the expanding fluid may be immediately spent in friction, without any appreciable portion of it being even temporarily employed to generate ordinary
vis viva
, or being devoted to produce sound. The non-conducting material was chosen to diminish as much as possible all loss of thermal effect by conduction, either from the air on one side to the air on the other side of the plug, or between the plug and the surrounding matter. A principal object of the researches is to determine the value of
μ
, Carnot’s function. If the gas fulfilled perfectly the laws of compression and expansion ordinarily assumed, we should have 1/
μ
= 1/E +
t
/J + Kδ/E
p
0
u
0
log P, where J is the mechanical equivalent of the thermal unit;
p
0
u
0
the product of the pressure in pounds on the square foot into the volume in cubic feet of a pound of the gas at 0° Cent.; P is the ratio of the pressure on the high pressure side to that on the other side of the plug; δ is the observed cooling effect;
t
the temperature Cent, of the bath, and K the thermal capacity of a pound of the gas under constant pressure equal to that on the low pressure side of the gas. To establish this equation it is only necessary to remark that Kδ is the heat that would have to be added to each pound of the exit stream of air, to bring it to the temperature of the bath, and is the same (according to the general principle of mechanical energy) as would have to be added to it in passing through the plug, to make it leave the plug with its temperature unaltered. We have therefore Kδ=—H, in terms of the notation used in the passage referred to.
A Porous Plug Method for the Mechanical Equivalent of Heat
