. Applied thermodynamics for engineers. reequal (Art. 108). 113. Ratio of Internal Energy Change to External Work. For any givenvalue of n, this ratio has the constant value n-1 114. Polytropic Paths. A name is needed for that class of pathsfollowing the general law 2wn=PV^, a constant. Since for anygas y and I are constant, and since for any particular one of thesepaths n is constant, the final formula of Art. Ill reduces to H = (S)(t-T).In other words, the rate of heat absorption or emission is directly pro-portional to the temperature change: the specific heat is constant. Suchpaths are cal
. Applied thermodynamics for engineers. reequal (Art. 108). 113. Ratio of Internal Energy Change to External Work. For any givenvalue of n, this ratio has the constant value n-1 114. Polytropic Paths. A name is needed for that class of pathsfollowing the general law 2wn=PV^, a constant. Since for anygas y and I are constant, and since for any particular one of thesepaths n is constant, the final formula of Art. Ill reduces to H = (S)(t-T).In other words, the rate of heat absorption or emission is directly pro-portional to the temperature change: the specific heat is constant. Suchpaths are called polytropic. A large proportion of the paths exempli-fied in engineering problems may be treated as polytropics. Thepolytropic curve is the characteristic expansive path for constantweight of fluid. 60 APPLIED THERMODYNAMICS 115. Relations of n and s. We have discussed such paths in which thevalue of 71 ranges from to infinity. Figure 31 will make the concep-tion more general. Let a represent the initial condition of the gas. If. Fig. 31. Art. 115. —Poly tropic Paths. it expands along the isothermal ab, n = 1, and s, the specific heat, is infi-nite ; no addition of heat whatever can change the temperature. If itexpands at constant pressure, along ae, n = 0, aud the specific heat is finiteand equal to hj = k. If the path is ag, at constant volume, n is infiniteand the specific heat is positive, finite, and equal to I. Along the isother-mal af (compression), the value of n is 1, and s is again infinite. Alongthe adiabatic ah, n = and s = 0. Along ai, n =: 0 and s = k. Alongad, n is infinite and s = I. Most of these relations are directly derivedfrom Art. 112, or may in some cases be even more readily apprehended bydrawing the adiabatics, en, gN^ fm, iM, dp, hP, and noting the signs of theareas representing heats absorbed or emitted with changes in any path lying between ah and af or between ac and ah, the specificheat is negative, the addition
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