First slide

Radiation

Question

Two spherical black bodies of radii R₁ and R₂ having surface temperatures T₁ and T₂ respectively radiate the same powers; then R₁/R₂ is equal to:

Moderate

A

${(\frac{T_{1}}{T_{2}})}^{4}$
B

${(\frac{T_{2}}{T 1})}^{4}$
C

${(\frac{T_{2}}{T_{1}})}^{2}$
D

${(\frac{T_{1}}{T_{2}})}^{2}$

Solution

$E_{1} = E_{2} σ 4 π {R^{2}}_{1} t {T_{1}}^{4} = σ 4 π {R^{2}}_{2} t {T^{4}}_{2} \frac{R_{1}}{R_{2}} = {\frac{T_{2}}{{T^{2}}_{1}}}^{2}$

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