Question

An incandescent lamp is made of a thin spherical glass bulb of diameter R_b = 30 mm, where vacuum is made, and with a filament in its center that radiates like a black body with power P = 40 W. The Stefan-Boltzmann constant is ? = 5.7 × 10?? W·m?²·K??; Planck's constant is h = 6.62 × 10?³? J·s; the speed of light is c = 3 × 10? m·s?¹. We consider first a filament that has a spherical shape with radius R_f = 1.5 mm. 1. Derive an expression for the filament's temperature T_f. 2. The wavelength at which the radiation is maximum is ? = 1.20 µm. Is the black body assumption justified? 3. Assuming that the thermal radiation is monochromatic, find the number j of photons received per second per unit surface of the light bulb. 4. In the steady state regime, the bulb, which acts as a black body for the emitted radiation and for the ambient radiation, is in thermal equilibrium at T_b = 350 K, while the air around it is at temperature T0 = 318 K. The thermal exchange at the glass/air interface is characterized by the convective heat transfer coefficient h_c = 6 W·K?¹·m?². Determine the fraction ? of the filament's radiation absorbed by the glass. 5. We now consider that the filament has a cylindrical shape of height l = 28 mm² and cross section s = 0.16 mm²; it is made of a material with electrical conductivity ? inversely proportional to its absolute temperature T. This filament of electrical conductivity ?? = 1.5 × 10? ??¹·m?¹ at temperature T? = 273 K, is connected to a generator with constant emf E = 2 V. Calculate the filament's temperature T in the steady state regime, neglecting the radition emitted by the glass bulb.

An incandescent lamp is made of a thin spherical glass bulb of diameter R_b = 30 mm, where vacuum is made, and with a filament in its center that radiates like a black body with power P = 40 W. The Stefan-Boltzmann constant is ? = 5.7 × 10?? W·m?²·K??; Planck's constant is h = 6.62 × 10?³? J·s; the speed of light is c = 3 × 10? m·s?¹.

We consider first a filament that has a spherical shape with radius R_f = 1.5 mm.

1. Derive an expression for the filament's temperature T_f.
2. The wavelength at which the radiation is maximum is ? = 1.20 µm. Is the black body assumption justified?
3. Assuming that the thermal radiation is monochromatic, find the number j of photons received per second per unit surface of the light bulb.
4. In the steady state regime, the bulb, which acts as a black body for the emitted radiation and for the ambient radiation, is in thermal equilibrium at T_b = 350 K, while the air around it is at temperature T0 = 318 K. The thermal exchange at the glass/air interface is characterized by the convective heat transfer coefficient h_c = 6 W·K?¹·m?². Determine the fraction ? of the filament's radiation absorbed by the glass.
5. We now consider that the filament has a cylindrical shape of height l = 28 mm² and cross section s = 0.16 mm²; it is made of a material with electrical conductivity ? inversely proportional to its absolute temperature T. This filament of electrical conductivity ?? = 1.5 × 10? ??¹·m?¹ at temperature T? = 273 K, is connected to a generator with constant emf E = 2 V. Calculate the filament's temperature T in the steady state regime, neglecting the radition emitted by the glass bulb.

$An incandescent lamp is made of a thin spherical glass bulb of diameter Rb = 30 mm, where vacuum is made, and with a filament in its center that radiates like a black body with power P = 40 W. The Stefan-Boltzmann constant is ? = 5.7 × 10?? W·m?²·K??; Planck's constant is h = 6.62 × 10?³? J·s; the speed of light is c = 3 × 10? m·s?¹. We consider first a filament that has a spherical shape with radius Rf = 1.5 mm. 1. Derive an expression for the filament's temperature Tf. 2. The wavelength at which the radiation is maximum is ? = 1.20 µm. Is the black body assumption justified? 3. Assuming that the thermal radiation is monochromatic, find the number j of photons received per second per unit surface of the light bulb. 4. In the steady state regime, the bulb, which acts as a black body for the emitted radiation and for the ambient radiation, is in thermal equilibrium at Tb = 350 K, while the air around it is at temperature T0 = 318 K. The thermal exchange at the glass/air interface is characterized by the convective heat transfer coefficient hc = 6 W·K?¹·m?². Determine the fraction ? of the filament's radiation absorbed by the glass. 5. We now consider that the filament has a cylindrical shape of height l = 28 mm² and cross section s = 0.16 mm²; it is made of a material with electrical conductivity ? inversely proportional to its absolute temperature T. This filament of electrical conductivity ?? = 1.5 × 10? ??¹·m?¹ at temperature T? = 273 K, is connected to a generator with constant emf E = 2 V. Calculate the filament's temperature T in the steady state regime, neglecting the radition emitted by the glass bulb.$

Added by Adedamola A.

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