188
CONDUCTION
OF
HEAT
— b) = RT, the equa- cooling itself. If px is taken still higher, the cooling decreases again, and we might take a value for px for v k tion of the isentropic curve follows as (^p + ^j( ~ b) = C, which the cooling would be zero, or even negative. If we call the energy per unit of weight e and the specific and from this we may deduce T(v — = C'. This latter volume v, the following equation holds :— relation shows in how high a degree the cooling depends e1+pLv1-piv2=e2, on the amount by which k surpasses unity, the change in or e1+p1v1 = e2+p2v2. v — b being the same. According to the symbols chosen by Gibbs, Xi = X2What has been said concerning the relative position of As % is determinedasby Tj and and Xi by T2 andp2> we obtain, the border-curve and the isentropic curve may be easily if we take Ti and p2 being constant, tested for points of the border-curve which represent dT, rarefied gaseous states, in the following way. Following GaXT#i Gt 1 ' 2") P2 T the border-curve we found before / — for the value of If T2 is to have a minimum value, we have Following the isentropic curve the value of I o (ta=“-(tx= Ti From this follows is equal to ^rrp If the isentropic curve rises O') more steeply than the border-curve. If we take /= 7 and SVlJ ^ choose the value of Tc/2 for T—a temperature at which is positive, we shall have to take for the maximum the saturated vapour may be considered to follow the gasMIX1 laws—then kk — 1 = 14, or &= 1-07 would be the limiting such a pressure that the product pv decreases with v, viz., value for the two cases. At any rate &= 1‘41 is great cooling a pressure larger than that at which pv has the minimum value. enough to fulfil the condition, even for other values of T. By means of the equation of state mentioned already, we find for Pictet has availed himself of this adiabatic expansion for the value of the specific volume that gives the greatest cooling, condensing many permanent gases, and it must also be the formula RT]5 2a used when, in the cascade method, T3 of one of the gases (Vj-6)2 v*’ lies above Tc of the next. A third method of condensing the permanent gases is and for the value of the pressure applied in Linde’s apparatus for liquefying air. Under a high pressure p1 a current of gas is conducted Linde’s we take the value 2TC for Tj, as we may approximately for apparatus. through a narrow spiral, returning through airIfwhen we begin to work with the apparatus, we find for px about another spiral which surrounds the first. Between the end of the first spiral and the beginning of the 8pc, or more than 300 atmospheres. If we take T1 = TC, as we may the end of the process, we find pi — 2.5pc, or 100 atmospheres. second the current of gas is reduced to a much lower at The constant pressure which has been found the most favourable pressure y>2 by passing through a tap with a fine orifice. in Linde’s apparatus is a mean of the two calculated pressures. On account of the expansion resulting from this sudden In a theoretically perfect apparatus we ought, therefore, to be able decrease of pressure, the temperature of the gas, and to regulate pi according to the temperature in the inner spiral. The critical temperatures and pressures of the permanent consequently of the two spirals, falls sensibly. If this process is repeated with another current of gas, this current, gases are given in the following table, the former being having been cooled in the inner spiral, will be cooled still expressed on the absolute scale and the latter in atmofurther, and the temperature of the two spirals will become spheres :— still lower. If the pressures px and remain constant the Pc L CH4 191-2°0 55 CO 133-5° 35-5 cooling will increase with the lowering of the temperature. 35 NO 179-5 71-2 lSr2 127° In Linde’s apparatus this cycle is repeated over and over 133° 39 02 155° 50 Air again, and after some time (about two or three hours) it Argon 152° 50‘6 H2 40° 20 becomes possible to draw off liquid air. According to Professor Dewar the critical temperature of H2 is The cooling which is the consequence of such a decrease about 32° absolute, and the critical pressure about 15 atmospheres of pressure was experimentally determined in 1854 by (Proc. Roy. Inst. Great Britain, 7th June 1899). (See also Liquid (j. d. v. d. W.) Lord Kelvin (then Professor W. Thomson) and Joule, who Gases.) represent the result of their experiments in the formula Conduction Of Heat.—The mathematical theory of conduction of heat was developed early in the 'TL '1T'2 —7Pi rp~P'1• 2 19th century by Fourier and other workers, and was In their experiments y?2 was always 1 atmosphere, and the brought to so high a pitch of excellence that little has amount of yq was not large. It would, therefore, be remained for later writers to add to this department of the certainly wrong, even though for a small difference in subject. In fact, for a considerable period, the term pressure the empiric formula might be approximately “theory of heat” was practically synonymous with the correct, without closer investigation to make use of it for mathematical treatment of conduction. A summary of the differences of pressure used in Linde’s apparatus, where Fourier’s analysis will be found in Heat (Ency. Brit. vol. px — 200 and y>2= atmospheres. For the existence of a xi.), and the theory need not be considered in detail here, most favourable value of px is in contradiction with the except in so far as it is required for the definition formula, since it would follow from it that Tx - T2 would and explanation of fundamental terms. The main object always increase with the increase of px. Nor would it be of the present article is to describe more recent work, right to regard as the cause for the existence of this most and to discuss experimental difficulties and methods of favourable value of px the fact that the heat produced in measurement. the compression of the expanded gas, and therefore pxlp2, 1. Mechanism of Conduction.—Conduction of heat immust be kept as small as possible, for the simple reason that plies transmission by contact from one body to another or the heat is produced in quite another part of the apparatus, between contiguous particles of the same body, but does and might be neutralized in different ways. not include transference of heat by the motion of masses Closer examination of the process shows that if p.} is or streams of matter from one place to another. This is given, a most favourable value of px must exist for "the termed Convection (see Radiation), and is most imFrom the equation of state (p +
