Normal body temperature is about 307K an Infrared detector w

Normal body temperature is about 307K. an Infrared detector which measures the power per area (R = P/A, where R=sigma*T^4) radiated from a small section of skin is sensitive to variations in R of 1%. What temperature difference can be detected?

Solution

the power per area is,

    R = sigma*T^4

so, we have the relation:

          R2/R1 = T2^4/T1^4

     1%R1/R1 = T2^4/(307)^4

            0.01= T2^4/(307)^4

               T2 = 97.08 K

Hence, the temperature difference: dT = 307 - 97.08 = 209.92 K = 210 K