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  4. An object is at a temperature of 400° C . At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible

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Q. An object is at a temperature of $ 400{}^\circ C $ . At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible

Rajasthan PETRajasthan PET 2001

Solution:

In first state, $ E=\sigma {{(673)}^{4}} $ In second state, $ 2E=\sigma {{T}^{4}} $ $ \therefore $ $ \frac{1}{2}={{\left( \frac{673}{T} \right)}^{4}} $ $ T={{(2)}^{1/4}}\times 673=800\,K $