Light bulb 1 operates with a filament temperature of 2800 K, whereas light bulb 2 has a filament temperature of 1700 K. Both fil
aments have the same emissivity, and both bulbs radiate the same power. Find the ratio A1/A2 of the filament areas of the bulbs. A1/A2
1 answer:
Answer:
A₁/A₂ = 0.136
Explanation:
The power radiated by a filament bulb is given by the following formula:
E = σεAT⁴
where,
E = Emissive Power
σ = Stephen Boltzman Constant
ε = emissivity
A = Area
T = Absolute Temperature
Therefore, for bulb 1:
E₁ = σε₁A₁T₁⁴
And for bulb 2:
E₂ = σε₂A₂T₂⁴
Dividing both the equations:
E₁/E₂ = σε₁A₁T₁⁴/σε₂A₂T₂⁴
According to given condition, the emissive power and the emissivity is same for both the bulbs. Therefore,
E/E = σεA₁T₁⁴/σεA₂T₂⁴
1 = A₁T₁⁴/A₂T₂⁴
A₁/A₂ = (T₂/T₁)⁴
where,
T₁ = 2800 K
T₂ = 1700 K
Therefore,
A₁/A₂ = (1700 K/2800 K)⁴
<u>A₁/A₂ = 0.136</u>
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