. Applied thermodynamics for engineers. ity of heat absorbed, and T the temperature of the isothermal. Ifthe temperature varies, the horizontal component of the path duringthe absorption of dlT units of heat is dn — dR-h T. For any pathalong which the specific heat is constant^ and equals k, kdT = dH^ , MT . T TdT J, T dn = —^, and n = Tcj^ _=^log^_. If the specific heat is variable, say k = a + hT, then 71. ^=«+J(r-o. The line hd of Fig. 47 is then a logarithmic curve, not a straightline; and the method of finding it adopted in Art. 158 is strictlyaccurate only for an infinitesimal chang
. Applied thermodynamics for engineers. ity of heat absorbed, and T the temperature of the isothermal. Ifthe temperature varies, the horizontal component of the path duringthe absorption of dlT units of heat is dn — dR-h T. For any pathalong which the specific heat is constant^ and equals k, kdT = dH^ , MT . T TdT J, T dn = —^, and n = Tcj^ _=^log^_. If the specific heat is variable, say k = a + hT, then 71. ^=«+J(r-o. The line hd of Fig. 47 is then a logarithmic curve, not a straightline; and the method of finding it adopted in Art. 158 is strictlyaccurate only for an infinitesimal change of temperature. Writingthe expression just derived in the form n = A;logg(^-T- t) and remem-bering that T= PV^ R^ while t = pv -^ R, we have n = k loge (P V-^ joi).The expression klog^^T-^f) is the one mostcommonly used for calculating values of the hori-zontal coordinate for polytropic paths. Theexpression dn = dH-^ T is general for all re-versible paths and is regarded by Rank in e asthe fundamental equation of 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
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