Thermodynamic exploration of an unconventional heat-engine cycle: the circular cycle

Abstract

The present paper applies both the first and the second laws of thermodynamics to the determination of the characteristics of an ideal diatomic gas heat engine that operates via a closed-loop circular cycle (viz of circular appearance in a P-V diagram when the pressure and volume units are appropriately scaled). The second law of thermodynamics reveals that an ideal gas undergoing an irreversible thermodynamic process P = P(V) with negative slope can reach a terminal point at d(PVγ)/dV = 0 without ever going to equilibrium with its environment. Furthermore, heat flows into the gas when d(PVγ)/dV>0 and out of the gas when d(PVγ)/dV<0. These conditions are then used to determine where Q = Qin and where Q = Qout for a circular work cycle. For a specimen engine, the efficiency is then obtained from the first law of thermodynamics.

Heat capacity of an ideal gas along an elliptical PV cycle

“…As has been pointed out by Dickerson and Mottmann 3 and Marcella and Sheldon, 8 given the symmetry of the cycle, the fact that the transfer of heat along the upper half of the cycle, Q(W→N→E;⌸), is positive while the transfer of heat along the lower half of the cycle, Q(E→S→W;⌸), is negative, could lead to the erroneous identification of these transfers of heat with the input heat flow, Q in , and the output heat flow, Q out , respectively. This erroneous identification can arise from an analysis based only on the first law of thermodynamics: because the gas expands ͑compresses͒ along the upper ͑lower͒ half part of the cycle, the work along this part is negative ͑positive͒.…”

“…Besides its intrinsic interest, understanding this behavior is essential in situations where a clear identification of the parts of a given path in which heat flows into or out of the system is necessary. [3][4][5][6][7] In the latter context, Marcella and Sheldon 8 have recently studied the efficiency of a heat engine with an ideal diatomic gas as the working fluid, operating through a circular cycle in a PV diagram. The points separating the part of the cycle where heat flows to the gas, QϭQ in , from that where heat flows from the gas, QϭQ out , are obtained from the condition d( PV ␥ )/dVϭ0, where ␥ϭC P /C V is the adiabatic coefficient of the gas, and C P and C V are assumed constant.…”

Unconventional cycles and multiple adiabatic points

“…Obtaining such point(s) is, in some cases, straightforward (the simplest, most discussed example is the linear, negative slope process [1][2][3][4][5][6]8]) while being difficult and error-prone in more complex cases (e.g. the circular [2,9,10], elliptical [11] and multilobed [12] cycles).…”

“…Although for the linear process, only a single [2] adiabatic point is allowed (because adiabatic curves cannot cross), numerical results show that more than two adiabatic points are possible on the circular cycle [10] (two such points were obviously necessary, albeit not always correctly located; see discussion in [2,9]). The possibility of several adiabatic points existing has attracted little attention, despite being a frequent question following the discussion of the linear process, and because the circular cycle usually resorts to numerical solutions, it is important to have an intermediate and treatable case.…”

An approach for determining thermal performance of the unconventional lobeP–Vcycles

“…Most studies and developments of the unconventional cycles are focused on demonstrating and understanding thermodynamic heat cycles such as triangle cycle [1][2][3][4], quasi-Carnot cycle with a linear P -V transition [1,5], circular cycle [2][3][4][5][6][7][8] and elliptical cycle [6] in the P -V plane. It is important to know the fact that the presentation of the P -V cycle may lead to a miscalculation of thermal efficiency if the wrong location of points in the P -V plane is used to evaluate the Q in and Q out [1,2,4].…”