A black body at a temperature $400$ K placed in an enclosure at $300$ K has cooling rate $r$ . If the temperature of the body were $800$ K and placed in the same enclosure, the cooling rate will be approximately:

2 r

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16 r

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23 r

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8 r

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Solution

The correct option is C $23 r$
Emissive power, $E = σ T^{4}$

$\frac{E}{r} = \frac{E_{2}}{E_{1}} = \frac{T_{2}^{4} - T_{e}^{4}}{T_{1}^{4} - T_{e}^{4}} = \frac{800^{4} - 300^{4}}{400^{4} - 300^{4}} = 22.94$

$E = 22.94 \times r$

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A black body at a temperature 400K placed in an enclosure at 300K has cooling rate r. If the temperature of the body were 800K and placed in the same enclosure, the cooling rate will be approximately:

The correct option is C 23rEmissive power, E=σT4Er=E2E1=T42−T4eT41−T4e=8004−30044004−3004=22.94E=22.94×r

A black body at a temperature $400$ K placed in an enclosure at $300$ K has cooling rate $r$ . If the temperature of the body were $800$ K and placed in the same enclosure, the cooling rate will be approximately:

The correct option is C $23 r$
Emissive power, $E = σ T^{4}$

$\frac{E}{r} = \frac{E_{2}}{E_{1}} = \frac{T_{2}^{4} - T_{e}^{4}}{T_{1}^{4} - T_{e}^{4}} = \frac{800^{4} - 300^{4}}{400^{4} - 300^{4}} = 22.94$

$E = 22.94 \times r$