A human body has a surface area of approximately 1 m 2 . The normal body temperature is 10 K above the surrounding room temperature T 0 . Take the room temperature to be T 0 = 300 K . For T 0 = 300 K

Question

A human body has a surface area of approximately 1 m 2 . The normal body temperature is 10 K above the surrounding room temperature T 0 . Take the room temperature to be T 0 = 300 K . For T 0 = 300 K , the value of σ T 4 = 460 W m 2 (where σ is the Stefan-Boltzmann constant). Which of the following options is/are correct?

TestHub · Accepted Answer

​ Energy radiated = σ A ( T 4 − T 0 4 ​ ) t = σ A [ ( T 0 ​ + 10 ) 4 − T 0 4 ​ ] t = σ A T 0 4 ​ [ ( 1 + T 0 ​ 10 ​ ) 4 − 1 ] t = σ A T 0 4 ​ [ T 0 ​ 40 ​ ] × t = 460 × 1 × 300 40 ​ × 1 = 61.33 J P = time Energy radiated ​ = σ A T 4 − σ A T 0 4 ​ ∴ ​ d T 0 ​ d p ​ ​ = σ A ( 4 T 0 3 ​ ) ∴ ∣ d p ∣ = σ A ( 4 T 0 3 ​ ) d T 0 ​ ∴ ∣Δ P ∣ = 4 σ A T 0 3 ​ ​ A, B are not correct options as human body is not a black body. Energy radiated ∝ A where A is the surface area of the body. ' C ' is the correct option

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