V J Menon

Lifetimes of Incandescent Bulbs

An article by Leff1 on incandescent bulbs has been very successful in illuminating the minds of not only physics students but also teachers. It has also prompted many articles that explore various aspects of incandescent lamps.2–9 An interesting topic discussed by Leff concerns lifetime statistics of bulbs by drawing analogy from radioactive decay of nuclei. Leff obtained an empirical formula for the survival probability of commercial bulbs and also hinted at the approximate equality of the half-life, the average life, and the most probable life of the same. While teaching this topic over the past few years, we found that the students were confused about the precise link between the survival and decay probabilities, and were also unable to derive the said equality of different lives as this problem was left in Ref. 1 as an exercise. The aim of this paper is to clarify these ideas.

Power of a finite speed Carnot engine

A model of an endoreversible Carnot engine is considered where the piston moves with a constant speed u. Expressions for the cycle time τ for the four branches, as well as output power, PW, are derived and the optimized root for maximum power is obtained in closed form. Our results are discussed in terms of the isothermal expansion ratio V*2 and temperature ratio a in a manner accessible to students.

Engines and refrigerators with finite heat reservoirs

The authors investigate the effect of finiteness of the heat reservoirs on the thermal efficiency of engines and performance coefficient of refrigerators, employing a Carnot cycle. The efficiency and the performance are both lowered in comparison to the case of machines working between reservoirs at constant temperatures.

Comment on `The Stefan-Boltzmann constant in n-dimensional space'

The expression for the Stefan-Boltzmann constant in n-dimensions as obtained by Landsberg and De Vos is modified by the appropriate spin-degeneracy factor of the photon.

The Carnot cycle with the van der Waals equation of state

The authors derive an expression for the efficiency of a Carnot engine using a van der Waals gas as the working substance.

On solving the Poisson equation for a `point' charge

In the context of the potential V due to a point charge we recapitulate the ambiguities associated with the Laplacian and the ansatze like 1/(r + b) with . Next, we show how to solve the Poisson equation starting from a standard representation of the radial delta function.

Physics of quiet and suffocative breathing

The process of breathing is analyzed theoretically by setting up and solving the hydrodynamic equation of motion for air flow, obtaining an expression for the work due to the pressure-drop, viscosity and drag, deriving relations for the effective length and cross section of the respiratory track, and deriving an expression for the surface energy generated in the lungs.

Thanks to the three viscous formulae

Many processes in everyday life, such as coating with shaving cream, the flow of water in town pipes, the clinical analysis of blood samples etc, are governed by viscosity. This is illustrated with the help of three classic formulae due to Newton, Poiseuille and Stokes.

The concept of enforced adiabats

Abstract We introduce a novel concept of enforced adiabatic paths along which the net heat absorbed vanishes, although the differential heat transfer need not. The mathematical criterion, comparison with the conventional adiabats, physical realisation, and possible application are discussed.

On the Euler angles for infinitesimal rotations

We address the problem of finding the Euler angles (a,b,c) connecting two Cartesian frames which are rotated infinitesimally (in the most general sense) with respect to each other. It is pointed out that while a + c and b are first-order small quantities, the angles a and c should be of order unity.