In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.
Since dE=dH - pdv, we have evidently for the variation of the total heat from the second expression (8), dF=d(E + pv) =dH+vdp=Sde - (Odv/de - v)dp .
We have therefore, by equation, (11), Sd0 = (Odv/d0 - v) d p,.
(15) where d0 is the fall of temperature of the fluid corresponding to a diminution of pressure dp. If there is no fall of temperature in passing the plug, d0 = o, and we have the condition Odv/d0 =v.