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Standard XII

Physics

Stefan-Boltzman's Law

The ratio of ...

Question

The ratio of rate of loss of heat by a black body at $227^{o}$ C to $127^{o}$ C in a surrounding at $27^{o}$ C is ____________.

25 : 16

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16 : 1

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3.108 : 1

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2.176 : 1

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Solution

The correct option is A $3.108 : 1$
Rate of heat transfer, $H \propto (T_{b o d y}^{4} - T_{S u r r}^{4})$

Thus, $\frac{H_{1}}{H_{2}} = \frac{T_{1}^{4} - T_{S u r r}^{4}}{T_{2}^{4} - T_{S u r r}^{4}} = \frac{500^{4} - 300^{4}}{400^{4} - 300^{4}} = \frac{{(5 / 3)}^{4} - 1}{{(4 / 3)}^{4} - 1} = 3.108$

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The ratio of rate of loss of heat by a black body at 227oC to 127oC in a surrounding at 27oC is ____________.

The correct option is A 3.108:1Rate of heat transfer, H∝(T4body−T4Surr)Thus, H1H2=T41−T4SurrT42−T4Surr=5004−30044004−3004=(5/3)4−1(4/3)4−1=3.108

The ratio of rate of loss of heat by a black body at $227^{o}$ C to $127^{o}$ C in a surrounding at $27^{o}$ C is ____________.