J.A. White

Optimization of heat engines including the saving of natural resources and the reduction of thermal pollution

The use of the new concept of a saving function as a measure of possible reductions of undesired side effects in heat engine operation is proposed. Two saving functions are introduced, one associated with fuel consumption and another associated with thermal pollution. Two optimization paths including the maximization of power output and these saving functions are presented. The first is based on a linear formalism and the second is based on a power-law formalism. When these optimization criteria are applied to a Curzon-Ahlborn heat engine, both criteria lead to a very similar optimum efficiency, opt = 1- 3/4 , where is the ratio between the temperatures of the cold and the hot external reservoirs. A numerical comparison with the efficiency of some modern nuclear power plants is reported.

Fluctuations in the number of particles of the ideal gas: A simple example of explicit finite-size effects

The fluctuations in the number of particles of the ideal gas are calculated using the canonical and the grand canonical ensembles. The two results differ by a factor which accounts for the relative size of the total volume and the subvolume where the canonical ensemble fluctuations are calculated. This factor gives a simple example of explicit finite-size effects, because it arises from considering a fixed number of particles in the canonical ensemble. Our simulation results for the isothermal compressibility of the hard disk fluid with a finite number of particles are improved by applying this correction.

On the quantum time autocorrelation functions

Abstract A relationship between the real and imaginary parts of an one-sided time autocorrelation function (TAF) of a hermitian operator is presented. On the basis of such relation, we suggest a simple way to take a semiclassical approach to express quantum TAFs. The obtained expressions are illustrated on two familiar examples in TAF formalisms.

A simple experiment for measuring bar longitudinal and flexural vibration frequencies

The sound wave in a cylindrical steel bar, generated by a light tap on one of its ends, is recorded by a microphone located near the other end. A sound analysis software is used to obtain the resonance spectrum of the bar. Longitudinal and flexural vibration frequencies are obtained from the peaks of the spectrum. The speed of sound, Young’s modulus, and Poisson’s ratio of steel are obtained.

Single-particle energy and velocity distributions for finite simple systems in the microcanonical ensemble

The probability distribution for the energy (velocity) of a particle in the microcanonical ensemble is obtained for some simple systems. Although in the thermodynamic limit the distribution has the well-known Boltzmann (Maxwell-Boltzmann) form (characteristic of the canonical ensemble), for finite systems this is not the case. This fact is important in the analysis of the results obtained from pedagogical computer simulations with a very small number of particles and constant total energy (i.e. simulations that generate the microcanonical ensemble).

Non-markovian far-infrared spectra of HF in liquid SF6

Non-markovian far-infrared spectra calculations for dilute solutions of HF in liquid SF6 at two different temperatures are presented in the range 0 to 250 cm-1. The fine rotational structure appearing in these spectra is discussed as function of the parameters involved in the theoretical absorption coefficient. A comparison with the spectra of other diatomic polar molecules (HCl, DCl) is also reported.

Numerical study of T 1 and T 2 rotational relaxation times of HCl in liquid Ar

Energy relaxation (T 1) and dephasing (T 2) processes are analysed for the rotational relaxation of diatomic polar molecules in rare-gas liquids under markovian assumption. Bath autocorrelation functions defining the markovian relaxation superoperator, which contains all information about T 1 and T 2 processes, are derived for an intermolecular potential approximated by a truncated series of Legendre polynomials P J . Hence, analytical expressions for T 1 and T 2 are obtained in terms of a reduced set of parameters regarding both the diatomic and the liquid as their mutual interaction. Numerical contribution to T 1 and T 2 processes, from P 1 and P 2 terms, is given for a HCl-Ar solution by using a dynamical quasiharmonic model to describe the solvent liquid structure.

Heat capacity of an ideal gas along an elliptical PV cycle

The heat capacity CΠ of an ideal gas along an elliptical cycle Π in a PV diagram is analyzed. We find that CΠ can take values between −∞ and +∞. The conditions CΠ=0 and CΠ=±∞ are used to determine the parts of the cycle where the transfer of heat has a positive or negative sign. The knowledge of CΠ 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.

Memory kernel for a multilevel quantum system driven by colored thermal noise

The memory kernel appearing in a non‐Markovian population equation for a multilevel quantum system stochastically coupled to a colored Gaussian bath is calculated on the basis of a fully quantum‐mechanical treatment to construct the time autocorrelation function (TAF) associated to the system–bath interaction Hamiltonian. The limiting cases of high and low temperatures and white noise bath are also analyzed. These examples allow us to discuss in a very simple way the dependence of the memory kernel on the Bohr frequencies of the system, the intensity of the system–bath interaction, its correlation time, and the bath temperature. In particular, it is shown that a true Markovian population equation is only achieved at high temperatures with a bath correlation time much shorter than the relaxation process characteristic time.

Memory effects on the rotational relaxation of diatomic polar molecules in non-polar liquids

Abstract A quantum study of the rotational energy relaxation ( T 1 ) and dephasing ( T 2 ) processes for diatomic polar molecules in a non-polar liquid host is given without invoking the Markovian hypothesis. The study is based on a model consisting of a rigid rotor stochastically coupled to a thermal bath. The time evolution of the reduced density operator of the rotor is described by a master equation with time-dependent matrix coefficients, which contains all information about the time dependence of the T 1 and T 2 rotational relaxation processes. Explicit expressions for the times characterizing these processes are derived on the basis of a quantum treatment for the time autocorrelation functions (TAF) of the rotor-bath interaction Hamiltonian. A numerical application for HCl in liquid Ar is also reported.