The rates of heat radiation from two patches of skin each of area A , on a patient's chest differ by 2 % . If the patch of the lower temperature is at 300 K and emissivity of both the patches is assumed to be unity, then what is the approximate temperature (in K ) of the other patch? [Ignore all the higher-order terms in approximation]

Question

The rates of heat radiation from two patches of skin each of area A , on a patient's chest differ by 2 % . If the patch of the lower temperature is at 300 K and emissivity of both the patches is assumed to be unity, then what is the approximate temperature (in K ) of the other patch? [Ignore all the higher-order terms in approximation],

MARKS App · Accepted Answer

According to Stefan's law. E 1 = σ T 4 a n d E 2 = σ T + ∆ T 4 ∴ E 2 - E 1 E 1 = σ [ T + ∆ T 4 - T 4 ] σ T 4 = 4 ∆ T T Now, E 2 - E 1 E 1 = 2 100 = 4 ∆ T 300 ∴ ∆ T = 300 × 2 4 × 100 = 1.5 K ∴ Temperature of other patch = T + ∆ T = 300 +1.5 = 301.5 K

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