Mechanics> Two uniform solid spheres A and B of same...

Two uniform solid spheres A and B of same material, painted completely black and placed in free space separately. Their radii are R and 2R respectively and the dominating wavelengths (wavelength corresponding to which spectral emissive power is maximum) in their spectrum are observed to be in the ratio 1 : 2. Which of the following is not correct. (1) Ratio of their temperatures is 2 : 1 (2) Ratio of their emissive powers is 4 : 1 (3) Ratio of their rates of heat loss is 4 : 1 (4) Ratio of their rates of cooling is 32 : 1 (5) None of these

Pranav Dabhade , 9 Years ago

Grade 12th pass

1 Answers

Yogendra Pawar

$\lambda$ ₁T₁ = $\lambda$ ₂T₂

T₁/T₂ = $\lambda$ ₂ / $\lambda$ ₁ = 2 : 1 (ratio of their temperature)

Rate of heat loss Q = 4 $\pi$ r² $\sigma$ $\varrho$ T⁴

(Q₁/Q₂ ) = (r₁/r₂ )² (T₁/T₂)⁴ = 4:1 (ratio of their heat loss)

Q= – msd $\theta$ /dt = – (4/3) $\pi$ r³ $\rho$ s d $\theta$ /dt

(d $\theta$ /dt)₁/ (d $\theta$ /dt)₂ = (Q₁/Q₂) (r₂/r₁)³ = 32:1 (ratio of their cooling rates)

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Mechanics> Two uniform solid spheres A and B of same...

Pranav Dabhade , 9 Years ago

Yogendra Pawar

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