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Heating a House

A house with no windows has walls which consists of thermal insulation with resistance tex2html_wrap_inline327 Kmtex2html_wrap_inline329/W surrounded by hard wall with total resistance tex2html_wrap_inline331 Kmtex2html_wrap_inline329/W. The area of the wall is A=80 mtex2html_wrap_inline329 how much power is required to heat the house to 60 F on a day when it is 32 F outside.

The total effective thermal resistance is
equation197
The power consumption is thus
equation200

Now keeping the same overall area the same we put in windows with thermal resistance tex2html_wrap_inline339 Kmtex2html_wrap_inline329/W and area tex2html_wrap_inline343 mtex2html_wrap_inline329. The new effective thermal resistance is obtained from the formula for parallel connection of thermal resistors:
eqnarray210
Note the large reduction in thermal resistance resulting from the small thermal resistance from the windows. This is the typical result of a parallel connection. The effective resistance is smaller than the smallest resistance involved. The corresponding rate of power consumption is now a factor tex2html_wrap_inline347 larger:
equation229


Collin Broholm
Mon Dec 8 11:41:49 EST 1997