. The steam-engine and other heat-motors . rent gases. For simplicity y is C generally used for the value of -^ for any gas. The equation for adiabatic expansion is then pvr=c. The work done during adiabatic expansion isP1V1-P2V2 r-i The total work of admission and expansion is PiV,+- r-i The net work done per stroke when there is no clearance andthe back pressure = the final pressure of expansion PiVi-PV r=P1V1-P2V2 + * ^ 2=-^i (PiV1-P2V2) = WKvT{Tl - T2) = WKP(T1 - T2) foot-pounds= TfCP(r1-772) T for perfectly dry air is tt= 1fiQ = X for moist air has some value between and 1
. The steam-engine and other heat-motors . rent gases. For simplicity y is C generally used for the value of -^ for any gas. The equation for adiabatic expansion is then pvr=c. The work done during adiabatic expansion isP1V1-P2V2 r-i The total work of admission and expansion is PiV,+- r-i The net work done per stroke when there is no clearance andthe back pressure = the final pressure of expansion PiVi-PV r=P1V1-P2V2 + * ^ 2=-^i (PiV1-P2V2) = WKvT{Tl - T2) = WKP(T1 - T2) foot-pounds= TfCP(r1-772) T for perfectly dry air is tt= 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,K2= VdP Kv~r~ PdVdVdP ~rv~~p- MEASURING THE EFFECTS OF HEAT. 143 Integrating, C — y log V = log P, C= y log 7+log P = log PW, To Draw the Curve PVn=C (Fig. 94).—Suppose the curve anda tangent at any point m is Fig. 94. Differentiate PVn = C. VndP + nP7n~1dV = 0 is the equation of the tangent. ?• dP=-nP-y, or jy=~nV From the figure, dP md md md cd de cd de From similar triangles, abbe n also. The minus sign shows that the angle, <£, that the tangent makeswith the X 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-section paper we find that the drawing of curves
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