Heat capacity of an ideal gas along an elliptical PV cycle

Abstract

A scaling approach to ideal quantum gases Am.A new microcomputer-based laboratory version of the Rüchardt experiment for measuring the ratio γ=Cp/Cv in air Am.The heat capacity C ⌸ of an ideal gas along an elliptical cycle ⌸ in a PV diagram is analyzed. We find that C ⌸ can take values between Ϫϱ and ϩϱ. The conditions C ⌸ ϭ0 and C ⌸ ϭϮϱ are used to determine the parts of the cycle where the transfer of heat has a positive or negative sign. The knowledge of C ⌸ allows us to do an analytical calculation of the transfer of heat during a process between two points along the cycle. The corresponding TS diagram is also discussed.

General formalism for calculating the thermal efficiency of thermodynamic cycles defined in a $p-V$ diagram

“…[4] and for the ideal gas along an elliptical p − V cycle in Ref. [5]. Similarly, to calculate the thermal efficiency, the use of logarithmic plots of the p−V diagram has been suggested in Ref.…”

Unconventional cycles and multiple adiabatic points

“…In this so-called adiabatic point, as the name indicates, the process P (V ) is tangent to an adiabatic curve 2 and δQ = 0. The simplest, most discussed example is the linear, negative slope process 1-6,8 while more complex cases involve circular 2,9,10 , elliptical 11 and multilobed 12 cycles. Although the linear case may only have a single 2 adiabatic point (because adiabatic curves cannot cross), there are numerical results showing that multiple adiabatic points are possible on the circular cycle 10 .…”

“…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).…”

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].…”

“…In the literature, there are several methods proposed to determine the adiabatic points. To the author's knowledge, these methods can be summarized as the tangential method [1,2], the heat capacity method [6][7][8][9][10], the direct method [7] and the entropy method [8]. In the tangential method, two requirements drive the development: the need for taking d(P V γ )/dV = 0 at adiabatic points, leading to a relationship of dP /dV = −γ P /V , and the need for having adiabatic points located on the profile.…”