A tungsten wire in a vacuum has length 15.0cm and radius 1.00mm. A potential dif

Question

A tungsten wire in a vacuum has length 15.0cm and radius 1.00mm. A potential difference is applied across it. (a) What is the resistance of the wire at 293K? (b) Suppose the wire reaches an equilibrium temperature such that it emits 75.0 W in the form of radiation. Neglecting absorption of any radiation from its environment, what is the temperature of the wire? (Note: e=0.320 for tungsten.) (c) What is the resistance of the wire at the temperature found in part (b)? Assume the temperature changes linearly over this temperature range. (d) What voltage drop is required across the wire? (e) Why are tungsten lightbulbs energetically inefficient as light sources?

Explanation / Answer

= 5.6 * 10-8 m ; = 0.004403

a) R = L/A = 2.675 m

b) From Stefen's Law, = 5.67*10-8

Power = e A T4 ; A = total surface area = 2*cross section + Cylindrical portion = 9.4828*10-4 m2

75 = 5.67*10-8 * 0.32 * 9.4828*10-4 * T4

T = 1445 K

c) R = Ro (1 + T) = 16.243 m

d) P = V*V/R -----> V = 1.1 Volts

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