Question

B. The silica cylinder of a radiant wall heater is 0.6 m long

Answer 1

So,  If the silica cyliner of the radiant wall heater is rated at 1.5 kw its temperature when operating is 1025.3 K

To estimate the operating temperature of the radiant wall heater, we need to use the equation for power radiated by the radiant wall heater.

Power radiated by the radiant wall heater

The power radiated by the radiant wall heater is given by P = εσAT⁴ where

• ε = emissivity = 1 (since we are not given),
• σ = Stefan-Boltzmann constant = 6 × 10⁻⁸ W/m²-K⁴,
• A = surface area of cylindrical wall heater = 2πrh where
• r = radius of wall heater = 6 mm = 6 × 10⁻³ m and
• h = length of heater = 0.6 m, and
• T = temperature of heater

Since P = εσAT⁴

P = εσ(2πrh)T⁴

Making T subject of the formula, we have

Temperature of heater

T = ⁴√[P/εσ(2πrh)]

Since P = 1.5 kW = 1.5 × 10³ W

Substituting the values of the variables into the equation, we have

T = ⁴√[P/εσ(2πrh)]

T = ⁴√[1.5 × 10³ W/(1 × 6 × 10⁻⁸ W/m²-K⁴ × 2π × 6 × 10⁻³ m × 0.6 m)]

T = ⁴√[1.5 × 10³ W/(43.2π  × 10⁻¹¹ W/K⁴)]

T = ⁴√[1.5 × 10³ W/135.72  × 10⁻¹¹ W/K⁴)]

T = ⁴√[0.01105 × 10¹⁴ K⁴)]

T = ⁴√[1.105 × 10¹² K⁴)]

T = 1.0253 × 10³ K

T = 1025.3 K

So, If the silica cylinder of the radiant wall heater is rated at 1.5 kw its temperature when operating is 1025.3 K

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