Consider a 150-W incandescent lamp. The filament of the lamp is 5 cm long and has a diameter of 0.5 mm. The diameter of the glass bulb of the lamp is 8 cm. Determine the heat flux in W/m2 on: (a) on the surface of the filament (b) on the surface of the glass bulb (use the assumption that the surface of the bulb can be approximated as a sphere with a diameter of 8 cm), and (c) calculate how much it will cost per year to keep that lamp on for eight hours a day every day if the unit cost of electricity is $0.08/kW

The answer is below

Explanation:

The heat flux or heat intensity is the flow of energy per unit area per unit time. measured in watts per meter² (W/m²).

a) The surface area of filament = πDL

D = diameter = 0.5 mm = 5 * 10⁻⁴ m, L = length = 5 cm = 5*10⁻² m

surface area of filament = π* 5 * 10⁻⁴ m * 5*10⁻² m = 25π * 10⁻⁶ m²

The heat flux on the surface of filament = 150 W / (25π * 10⁻⁶ m²) = 1.91 * 10⁶ W/m²

b) Since the glass tube is a sphere with diameter = 8 cm;

radius (r) = diameter / 2 = 4 cm = 4* 10⁻² m

Surface area of glass tube = 4πr² = 4π * (4* 10⁻²)²  = 64π* 10⁻⁴ m²

The heat flux on the surface of filament = 150 W / (64π* 10⁻⁴ m²) = 7.46 * 10³ W/m²

c) The total energy consumed in a year = 150 W * 365 days * 8 hours/day =  438000 Wh = 438 kWh

Cost of energy = unit cost * energy consumed = $0.08/kW * 438 kWh = $35.04

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