Question

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. Provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20 ℃ throughout the year, while the walls of the room are nominally at 27 ℃ and 14 ℃ in the summer and winter, respectively. The exposed surface of a person in the room may be assumed to be at a temperature of 32 ℃ throughout the year and to have an emissivity of 0.90. The coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 W/m2∙K.

Answer 1

radiative heat loss substantially increases as the wall temperature declines

Step-by-step explanation:

The body's heat loss due to convection is ...

(2 W/m^2·K)((32 -20)K) = 24 W/m^2

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The body's heat loss due to radiation in the summer is ...

`\epsilon\sigma(T_b^4-T_w^4)\quad\text{where $T_b$ and $T_w$ are body and wall temperatures ($^\circ$K)}\\\\0.90\cdot 5.6703\cdot 10^(-8)(305.15^4-300.15^4)\,\text{W/m$^2$}\\\\\approx 28.3\,\text{W/m$^2$}`

The corresponding heat loss in the winter is ...

`0.90\cdot 5.6703\cdot 10^(-8)(305.15^4-287.15^4)\,\text{W/m$^2$}\\\\\approx 95.5\,\text{W/m$^2$}`

Then the total of body heat losses to surroundings from convection and radiation are ...

summer: 24 +28.3 = 52.3 . . . W/m^2

winter: 24 +95.5 = 119.5 . . . W/m^2

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It is reasonable that a person would feel chilled in the winter due to the additional radiative loss to the walls in the winter time. Total heat loss is more than doubled as the wall temperature declines.