Question

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

• A. $301.5K$
• B. $306K$
• C. $308.5K$
• D. $312K$

Answer 1

Answer: (A)

$301.5K$

$P=\sigma eA{T}^4$

$\frac{P_1}{P_2}=(\frac{T_1}{T_2}{)}^4\frac{P+P\times \frac{2}{100}}{P}=(\frac{T_1}{300}{)}^{4}1+\frac{2}{100}=(\frac{T_1}{300}{)}^4\Rightarrow \frac{102}{100}=(\frac{T}{300}{)}^4\Rightarrow T=301.488K\simeq 301.5K$