First slide

Radiation

Question

The rate of heat radiation from two patches of skin each of area S, on a patient's chest differ by 2%. lf the patch of the lower temperature is at 300 K and the emissivity of both the patches is assumed to be unity, the temperature of the other patch is closest to

Moderate

A

301.5 K
B

306 K
C

308.5 K
D

312 K

Solution

Here $E_{1} = {σT}^{4}$
and $E_{2} = σ (T + ΔT)^{4}$
$∴ \frac{E_{2} - E_{1}}{E_{1}} = \frac{4 ΔT}{T} = \frac{2}{100}$
or $\frac{4 \times ΔT}{300} = \frac{2}{100} or ΔT = 1 \cdot 5 K$
$∴ T + ΔT = 300 + 1 \cdot 5 = 301 \cdot 5 K$

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