. The steam-engine and other heat-motors. ferent gases. For simplicity y is Cgenerally used for the value of -^ f°r any gas. The equation for adiabatic expansion is then PVr = C. The work done during adiabatic expansion is P1V1-P2V2 r-i The total work of admission and expansion is PiV1-P2V2 PiV1 + r The net work done per stroke when there is no clearance andthe back pressure = the final pressure of expansion =PiVi-P2V2+PlVlrZ^2 = -jri (PxVl-P2V2) = WKvT(T1 - T2) = WKP(T1 - T2) foot-pounds= WCV(T1-T2) X for perfectly dry air is 7r= 1fiq = X for moist air has some value between
. The steam-engine and other heat-motors. ferent gases. For simplicity y is Cgenerally used for the value of -^ f°r any gas. The equation for adiabatic expansion is then PVr = C. The work done during adiabatic expansion is P1V1-P2V2 r-i The total work of admission and expansion is PiV1-P2V2 PiV1 + r The net work done per stroke when there is no clearance andthe back pressure = the final pressure of expansion =PiVi-P2V2+PlVlrZ^2 = -jri (PxVl-P2V2) = WKvT(T1 - T2) = WKP(T1 - T2) foot-pounds= WCV(T1-T2) X for perfectly dry air is 7r= 1fiq = X for moist air has some value between and The equation PVr = C may be easily derived from the twofundamental equations of thermodynamics derived on page 152: H=KpdT-VdP,H = KvdT+PdV. When the expansion is adiabatic H = 0: KpdT=VdP,KvdT= -PdV,Kj,= VdP Kv r~ PdVdVdP ry- P> MEASURIXG THE EFFECTS OF HEAT. 143 Integrating, C — y log V = log P, C=y\ogV+\ogP = log PVr,Ct = PVr. To Draw the Curve PYn = C (Fig. 94).—Suppose the curve anda tangent at any point m is Fig. 94. Differentiate PV»=C. VndP + nP7n~ldV = 0 is the equation of the tangent. jt> i>dV dP P dP= —nP-yr, or ly—~ny- From the figure, md o From similar triangles, dPmd dV c?e md m cd _de cd de abbe = — n also. The minus sign shows that the angle, , that the tangent makeswith the A axis, if measured from the X axis to the tangent, isgreater than 90 degrees. Given one point on the curve and n, thevalue of C may be calculated. For any assumed V, the corre- 144 THE STEAM-ENGINE AND OTHER HEAT-MOTORS. sponding P may be calculated, and then if be and cd be assumedto be those values, de and ab may be laid off so that the tangentmay be drawn. Having a series of points and the tangents, thecurve may be drawn through the points and tangent to the tangents. Logarithmic Cross-section Paper and PVn Curves.—Loga-rithmic cross-section paper is invaluable in work dealing withequations of the form PVn = C. By the use of this kind of cross-sect
Size: 1784px × 1401px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublisheretcetc, booksubject
