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Find the net rate of heat transfer by radiation from a skier standing in the shade. The skier is completely clothed in white with an emissivity of 0.200, a surface temperature of 10.0ºC, surroundings at −15.0ºC, and a surface area of 1.60 m².

a) -97.4 W
b) -78.6 W
c) -61.2 W
d) -45.8 W

Answer :

Final answer:

The net rate of heat transfer by radiation from a skier is found using the Stefan-Boltzmann law and the given parameters. The calculation yields a net heat transfer rate of approximately -97.4 W, which aligns with option (a).

Explanation:

The net rate of heat transfer by radiation from a skier standing in the shade can be determined using Stefan-Boltzmann law for radiation. The equation used is Q = ε∙A∙σ(∙T_{1}^{4} - T_{2}^{4}), where Q is the net heat transfer rate, ε is the emissivity of the surface, A is the surface area, σ is the Stefan-Boltzmann constant (5.67 x 10^{-8} W/m^2K^4), T_{1} is the surface temperature of the skier in Kelvin, and T_{2} is the surroundings' temperature in Kelvin.

To transform the temperatures from Celsius to Kelvin, we add 273.15. The skier's surface temperature is therefore 283.15 K (10.0°C + 273.15) and the surroundings is 258.15 K (-15.0°C + 273.15).

Using the given values:

  • Emissivity, ε = 0.200
  • Surface area, A = 1.60 m²
  • Skier's surface temperature, T_{1} = 283.15 K
  • Surroundings temperature, T_{2} = 258.15 K

The net rate of heat transfer by radiation is:

Q = (0.200)∙(1.60 m²)∙(5.67 x 10^{-8} W/m^2K^4)∙((283.15 K)^4 - (258.15 K)^4)

Q ≈ -97.4 W

Thus, the net heat transfer by radiation is approximately -97.4 W, which corresponds to option (a).

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