. Applied thermodynamics for engineers. Fig. 51. Art. 1( Graphi-of cal DeterminationSpecific Heat. 164. Computation of Specific Heat. If at arxy point on a reversible path a tangent be drawn, the length of the subtangent on the iV-axis represents thevalue of the specific heat at that point. In Fig. 51, draw the tangent nm to thecurve ^i5 at the point nand construct the infinitesimaltriangle dtdn. From similar triangles, mrr::dn: dt,or mr = Tdn --• dt = dU ^ dt = s (Art. 112). 165. Comparison of Specific Heats. If a gas is heated at constant pressure from a, Fig, 52, it willgain heat and te
. Applied thermodynamics for engineers. Fig. 51. Art. 1( Graphi-of cal DeterminationSpecific Heat. 164. Computation of Specific Heat. If at arxy point on a reversible path a tangent be drawn, the length of the subtangent on the iV-axis represents thevalue of the specific heat at that point. In Fig. 51, draw the tangent nm to thecurve ^i5 at the point nand construct the infinitesimaltriangle dtdn. From similar triangles, mrr::dn: dt,or mr = Tdn --• dt = dU ^ dt = s (Art. 112). 165. Comparison of Specific Heats. If a gas is heated at constant pressure from a, Fig, 52, it willgain heat and temperature, following some suchpath as ah. If heated at constant volume,through an equal range of temperature^ a less. Fig. 52. Art. 165. —Com-parison of Specific Heats. ENTROPY 97 quantity of heat will be gained; the subtended area aefd will be lessthan the area abed. In general, the less the specific heat, the morenearly vertical will be the path. (Compare Fig. 49.) When A: = 0, thepath is vertical; when k = cc, the path is horizontal. 166. Properties of the Carnot Cycle. In Fig. 48, it is easy to see thatsince efficiency is equal to net expenditure of heat divided by gross ex-penditure, the ratio of the areas abde and abjSfn expresses the efficiency,and that this ratio is equal to {T—t)-r- T. The cycle abde is obviouslythe most efficient of all that can be inscribed between the limiting iso-thermals and adiabatics. 167. Other Deductions. The net enclosed area on the TN diagramrepresents the net movement of heat. That this area is always equivalentto the corresponding enclosed area on the PF diagram is a statement ofthe first law of thermodynamics. Two statements of the second law havejust
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