Heat Transfer - Radiation: Practice Problem & Solution
Assertion (A): If temperature of any body is increased by \(10\%\), then there will be \(40\%\) increase in amount of radiation from its surface. Reason (R): Equation \(\frac{\Delta E}{E} = 4 \frac{\Delta T}{T}\) also the for large percentage increase where \(E \propto T^4\).
Solution Explained:
To solve this problem, we apply the core principles of Heat Transfer - Radiation. Understanding the underlying formula is key to arriving at the correct answer below:
According to the Stefan-Boltzmann law, `\(E \propto T^4\)`. If `\(T\)` increases by `\(10\%\)`, the new temperature `\(T' = 1.1T\)`. Then `\(E' \propto (1.1T)^4 = 1.4641T^4\)`. The percentage increase is `\(46.41\%\)`. So, Assertion (A) is false. The approximation `\(frac{\Delta E}{E} = 4 \frac{\Delta T}{T}\)` is valid only for small percentage changes in temperature, not for 'large' changes like `\(10\%\)`. Therefore, Reason (R) is also false.
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