. Applied thermodynamics for engineers. he pathwill be similar to ai or aj\Fig. 48. If the specificheat is negative, the tem-perature will increase withrejection of heat, or de-crease with its absorption, as along the paths ak, al, Fig. 48. Theseresults may be compared with those of Art. 115. Figure 49 showson the new diagram the. paths corresponding with those of Fig. may be noted that, in general, though not invariably, increases of / u / ^ / ^./ HI o/^ < N Fig. 49. Arts. 161, 165. —PolytropicEntropy Diagram. *aths on ENTROPY 95 volume are associated with increases of the horigionta
. Applied thermodynamics for engineers. he pathwill be similar to ai or aj\Fig. 48. If the specificheat is negative, the tem-perature will increase withrejection of heat, or de-crease with its absorption, as along the paths ak, al, Fig. 48. Theseresults may be compared with those of Art. 115. Figure 49 showson the new diagram the. paths corresponding with those of Fig. may be noted that, in general, though not invariably, increases of / u / ^ / ^./ HI o/^ < N Fig. 49. Arts. 161, 165. —PolytropicEntropy Diagram. *aths on ENTROPY 95 volume are associated with increases of the horigiontal coordinate ofthe new diagram. 162. Justification of the Diagram. In the PV diagram of Fig. 50, considerthe cycle ABCD. Let the heat absorbed along a portion of this cycle be repre-sented by the infinitesimal strips nabN,NbcM, Mcdm, formed by the indefinitelyprojected adiabatics. In any one of thesestrips, as nabN, we have, in finite terms, nahN _ T nabN _ negN negN~ t T ~ t Considering the whole series of stripsfrom A to C, we have. x;^ nahN _ -^ negN Fig. 50. Art. 162. —Entropy a CardinalProperty. or, using the symbol H for heat trans-ferred, dH 5^ = 0, in which T expresses temperature generally. Let the substance complete the cycle ABCDA; we then have, the paths beingreversible. ^ dH _ \ dH I dH r, A fjA • kJo while for the cycle AD CD A whence, dH _ \ dH ^ I I -T- \ -r+ I A xJa kJg I ^- I ^ Y T~ Y T The integral f ^ thus has the same value whether the path is ADC or ABC, or, indeed, any reversible path between A and C; its value is independent of thepath of the substance. Now this integral will be shown immediately to be the mostgeneral expression for the horizontal coordinate of the diagram under it denotes a cardinal property, like pressure or temperature, it is permissible to use a diagram in w:hich the coordinates are T and f-^* 96 APPLIED THERMODYNAMICS 163. Analytical Expression. Along any path of constant tem-perature, as ah^ Fig. 48, the hori
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