A man, the surface area of whose skin is 2 m2 , is sitting in a room w

1.	A man, the surface area of whose skin is 2 m2 , is sitting in a room where air temperature is 20ºC and emissivity of his skin equal 0.97, find the rate at which his body loses heat. (Give H = 5.67 × 10-8 Wm-2 K-4 )
Answer» We have H = σεA(T⁴ – T₀⁴ ) Here, T = (28 + 273) K = 301 K T₀ = (20 + 273)K = 293 K H = (5.67 × 10^-8 Wm^-2 K^-4 ) × 0.97 × 2m² [(301k)⁴ – (293K)⁴ ] = 92.2 W Here, since (T - T₀) is small, let us also calculate H by using the approximate form of Stefan Boltzmann law. We have H = σεA(T - T₀) = 5.67 × 10^-8 × 0.97 × 2 × 17 W = 88 W The approxmate value is thus (nearly) 4.3% lower than its more exact value.

A man, the surface area of whose skin is 2 m2 , is sitting in a room where air temperature is 20ºC and emissivity of his skin equal 0.97, find the rate at which his body loses heat. (Give H = 5.67 × 10-8 Wm-2 K-4 )

Answer»

We have

H = σεA(T⁴ – T₀⁴ )

Here, T = (28 + 273) K = 301 K

T₀ = (20 + 273)K

= 293 K

H = (5.67 × 10^-8 Wm^-2 K^-4 ) × 0.97 × 2m² [(301k)⁴ – (293K)⁴ ]

= 92.2 W

Here, since (T - T₀) is small, let us also calculate H by using the approximate form of Stefan Boltzmann law. We have

H = σεA(T - T₀)

= 5.67 × 10^-8 × 0.97 × 2 × 17 W

= 88 W

The approxmate value is thus (nearly) 4.3% lower than its more exact value.