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Chapter 3: Q69E (page 578)

The operating temperature of a tungsten filament in an incandescent light bulb is 2450 K, and its emissivity is 0.350. Find the surface area of the filament of a 150-W bulb if all the electrical energy consumed by the bulb is radiated by the filament as electromagnetic waves.

Short Answer

Expert verified

The filament area of a 150 W bulb is 2.1脳104m2.

Step by step solution

01

Given Data

Operating temperature: 2450 K

Emissivity: 0.350

Power: 150 W

02

Concept/Significance of Wien’s displacement

Following Wien's displacement rule, black body radiation has distinct temperature maxima at various wavelengths.

03

Determination of Find the surface area of the filament of a 150-W bulb

According to the Wien鈥檚 displacement area of the filament is given by,

H=A蔚蟽T4A=H蔚蟽T4

Here, H is the electrical energy, 蔚is the emissivity of bulb, 蟽 is the Stefan Boltzmann constant whose value is and T is the temperature.

Substitute all the values in the above equation.

A=150W0.350脳5.67脳10-8W/m2.K4脳2450K4=2.1脳10-4m2

Thus, the area of filament of the 150 W bulb is 2.1脳10-4m2.

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