The Relation between Efficiency and Life of the Tungsten Lamp

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  • タングステン電球の能率と寿命との関係

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It seems to be very commou to represent the relation between the efficiency and life of a tungsten lamp having the filament of a given size in such an exponential formula as l/lo=(eo/e) k where l and lo are the life at the efficiencies e and eo respectively, and k, usually called the life exponent, may vary according to the properities as well as the diameter of the filament and is considered as a constant for a given kind of lamps. Whether or not the above formula really represents the relation between the efficiency and life of an actual lamp may be determined by the experimental facts only. Two kinds of lamps, A and B, of different makers were tested at various efficiencies to obtain the relation between the efficiency and life. Lamp A, on the one hand, has given the results which conform the above formula and the value of the exponent may be considered as a constant throughout the wide range of efficiency. For lamp, B, on the other hand, the relation between the efficiency and life is not represented by the exponential formula, or the value of the exponent must be considered to vary with the efficiency.<BR>The life of a tungsten lamp is chiefly determined by the rate of vaporization of tungsten and we may calculate the life of a lamp if we know the necessary conditions. We have calculated the life at various efficiencies under the assumption that any filament burns out when the current passing through it decreases to a certain definite ratio of the initial value and determined the relation between the efficiency and life of an ideal tungsten lamp. The relation obtained may be expressed by an exponential formula and the value of the exponent were found to be 7.5. The exponent of an actual lamp ranges from 6.6 of smaller filament lamp to 7.4 of larger filament one. The discrepancy between the calculated and actual values of the exponent may be explained by considering the mechanical cause ef breakage of the filament is more probable in lamps burned at lower efficiencies, i. e. the lamps of longer life than in lamps of higher efficiencies and shorter life. This consideration will also be applicable to the question why the exponent ef smaller filament: lamps is smaller than that of larger filament ones.

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