D. C. Agrawal

Efficiency and efficacy of incandescent lamps

Planck’s radiation formula is used to estimate the dimensionless efficiency of incandescent lamps as a function of filament temperature, with typical values of 2%–13%. Similarly, using the known spectral luminous efficiency of the eye, the efficacy of incandescent light bulbs is estimated as a function of temperature, showing values of 8–24 L W−1 for bulbs of 10–1000 W. The efficiency and efficacy results compare favorably with published data and enable estimation of the filament temperature for any lamp of known efficacy.

Lifetime and Temperature of Incandescent Lamps.

Assuming that during the rated lifetime of a bulb roughly half of the radius of the filament evaporates, we can estimate the mean rate of evaporation. The filaments operating temperature can then be deduced from the Catalogue using linear interpolation. The probable reasons for the bulbs failure are also mentioned.

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.

SWITCHING TIME OF A 100 WATT BULB

The switching time of a bulb, i.e. the time taken to achieve a state of full brilliance after being turned on, is of considerable pedagogical interest. To estimate this time we take the resistance and heat capacity of the filament as suitably parametrized functions of the temperature and solve a simplified heat equation. A numerical comparison is made with the experimental data on a 100 watt bulb.

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.

Light bulb exponent-rules for the classroom

Exponent-rules are known to describe experimentally how the observables related to incandescent lamps alter with the change in the rated voltage. Pedagogical derivation of the rules for typical observables like the life, lumens, power, etc. in the case of vacuum bulbs is presented. This is achieved by assuming a steady-state operation of the bulb, parameterizing intrinsic properties of tungsten as suitable powers of temperature, and eliminating the temperature between those observables for which the exponent-rules are sought.

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.

A finite speed Curzon–Ahlborn engine

Curzon and Ahlborn achieved finite power output by introducing the concept of finite rate of heat transfer in a Carnot engine. The finite power can also be achieved through a finite speed of the piston on the four branches of the Carnot cycle. The present paper combines these two approaches to study the behaviour of output power in terms of isothermal expansion ratio V*2 and the temperature differences x and y present at the hot source and cold sink branches, respectively, for the benefit of undergraduate students.

A Theory for the Mortality Curve of Filament Lamps

We demonstrate for the first time that the ejection of tungsten atoms from a hot filament can be modeled by a binomial distribution. The relevant ejection chance per atom may have an arbitrary temporal profile depending on the presence of uniform Richardson evaporation, hot spots and temperature variation along the wire. A normal approximation is made and the lamp is supposed to fail if the undecayed atomic fraction drops below a critical value. The resulting formula for the lamp’s survival probability in terms of error function has one free parameter and is shown to be in excellent agreement with the experimental mortality curve.

Work and heat expenditure during swimming

The act of treading water, or swimming in an upright position, is examined. The hydrodynamic resistance involved and the amount of work done by the muscles are discussed. The mechanisms of heat loss and the corresponding expression for heat loss are also described. These points are illustrated with a numerical example.