NEET Physics Question - Thermal Physics - Heat Transfer

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 \(E \propto T^4\).

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

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.

Rankers Physics

Radiation and Temperature Change

Solution:

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