Reflections on the pedagogic motive power of unconventional thermodynamic cycles

Abstract

Pedagogic niceties in the treatment of unconventional thermodynamic cycles, especially those involving (negatively sloping) diagonal linear transitions in a P/V state diagram and/or those implying supposedly superefficient heat-engine operation, are discussed as a means of stimulating student interest and comprehension, as well as promoting fresh insights, correcting erroneous notions, and provoking further enquiry. In particular, a novel (ostensibly all-adiabatic) engine using two ideal gases of mutually differing atomicities as working substance is analyzed qualitatively and quantitatively. Emphasis is placed on the crucial role of the second law of thermodynamics in a determination of heat-engine operation.

The Specific Heats of Gases in an Arbitrary Process

“…and ( ) ∂ ∂ P T T may be calculated from the equation of state for a gas and d d F v may be derived from equation 8specifying an arbitrary process. Therefore, equation (11) gives the specific heat of gases in any arbitrary process. It is a very general expression, from which many useful results can be derived.…”

“…Using equation (11) and the equation of state of ideal gases, we can obtain the specific heat of ideal gases in an arbitrary process as [6] c c R P…”

“…This equation holds fairly well in the liquid region, the vapour region, and near and above the critical point [1]. From equations (11) and (17), we obtain the specific heat of the Van der Waals gas in an arbitrary process as…”

The P–V Linear Expansion of an Ideal Gas

“…Since the P-V linear expansion of the gas has already been comprehensively analysed in the P-V diagram in previous literature [1,[5][6][7][8], in this paper the expansion of the gas is tackled mainly following the T-S representation, in which the heat flow to and from the gas can be straightforwardly read.…”

Heat capacity of an ideal gas along an elliptical PV cycle

“…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.…”