. The steam-engine and other heat-motors. e inthe intrinsic energy of the gas, whilst dL represents the work ofmolecular separation and dU represents external or visible workSome heat must be expended in separating even the molecules ofperfect gases, since they must have some attraction for one anotherbecause they have mass. In practical work this is small enoughto be neglected. : MEASURIXG THE EFFECTS OF HEAT. 153 Let ade . . represent the path of the gas. Through the pointsa, d, e, . . pass both an isothermal and an adiabatic. The areabetween the adiabatic and the base is in each case equal
. The steam-engine and other heat-motors. e inthe intrinsic energy of the gas, whilst dL represents the work ofmolecular separation and dU represents external or visible workSome heat must be expended in separating even the molecules ofperfect gases, since they must have some attraction for one anotherbecause they have mass. In practical work this is small enoughto be neglected. : MEASURIXG THE EFFECTS OF HEAT. 153 Let ade . . represent the path of the gas. Through the pointsa, d, e, . . pass both an isothermal and an adiabatic. The areabetween the adiabatic and the base is in each case equal to the heatin the gas. At a the heat in the gas is KVTX) at d the heat in thegas is Kv(Tx+dT). The work done badc = PdV. Let c/# = heatadded. Then KVTX +dH = Kv(T1 +dT) +PdV dH=KvdT-PdV. To derive the formula dH = KpdT-YdP. Let ade ... be the path of the fluid. Through a draw anisothermal 7\ and an adiabatic. Let the next higher isothermal7\ + dT be df. The heat in the gas at a=KvTx. The heat in the gas at f=Kv(Tx+dT). The heat added. Fig. 102. KvdT+bafg = KpdT. The path of the fluid is from a to d, however. The heat in| the gas at d and / is the same since those points are on thesame isothermal. To reach the point d from / the gas must becooled or heat must be subtracted equal to the area dcgf. Since df is an isothermal, (dc)X(dk) = (fg)X(fh). Subtract? the common area (hm)X(mc) and we have kdmh = mfgc. Addingthe common area dfm to each side and we have kdfh = dcgf, but1 kdfh = VdP; therefore the heat expended, dH, =KpdT-VdP. 154 THE STEAM-ENGINE AND OTHER HEAT-MOTORS. Carnot Cycle.—The term cycle may be used to indicate a periodof time in which a series of events repeat themselves; a closed figurethat may be a graphic description of a recurring series of events,or a series of operations bringing the thing operated upon to itsoriginal state. The Carnot cycle is a cycle of operations per-formed on a perfect gas working in an engine of perfect mechan-ical efficiency, and it wi
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