In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a positionmeasuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics.

Analyzing a process in terms of entropy production is shown to provide a quantitative approach to the second law of thermodynamics. The second law, ΔS≥0, is applied to the work–entropy relation obtained by rewriting the first law of thermodynamics in terms of the total entropy increase. The significance of entropy in macroscopic thermodynamics is established, and the limitations imposed by the second law are made evident. Irreversibility, entropy production, and the degradation of energy are seen as manifestations of the second law. The work–entropy relation indicates that entropy-producing irreversibilities are always accompanied by an amount of energy Wlost=TΔS that becomes unavailable to do work. The Kelvin–Planck and Clausius forms of the second law, as well as Carnot’s principle and the inequality of Clausius, are obtained from the work–entropy relation. It is shown that the increase in entropy for a system is due both to heat flowing into it, and to internal irreversibilities. Availability and the second-law efficiency are discussed.

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 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.

In a recent article in this journal, Brown and Singh present the results of an extensive in-class survey of student difficulties with the second law of thermodynamics. Here, we discuss in detail some issues identified by them in an attempt to resolve some of the problems. We do this by making clear the distinction between the ‘system entropy’, ‘reservoir entropy’, ‘total entropy’, and the ‘entropy of the universe’. We identify, without ambiguity, which quasistatic processes are ‘internally reversible’, which are ‘totally reversible’, and which are ‘irreversible’. We discuss the meaning of quasistatic processes represented by curves in the PV plane. We show that the process P=P(V) that takes an ideal gas from initial state (P_A V_A) to final state (P_B V_B) always takes the gas away from the adiabat PV^γ=P_A V_A^γ. We establish the increasing (total) entropy principle as the quantitative expression of the second law of thermodynamics. This establishes the fundamental role of the total entropy in macroscopic thermodynamics. Expressing the increasing (total) entropy principle in the form 〖(T〗_res-T_gas)d(PV^γ)>0 reveals which processes are allowed, which are not, and which points in the PV plane are accessible from a given initial state. Students can now observe the limitations on individual processes mandated by the second law. Such second law analysis is suitable for the introductory physics course.

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