The equations for heating a house are given by Eqs. (2.81) and (2.82), and in
a particular case can be written with time in hours as where
(a) C is the thermal capacity of the house, BTU/â—¦F,
(b) Th is the temperature in the house, â—¦F,
(c) To is the temperature outside the house, â—¦F,
(d) K is the heat rating of the furnace, = 90, 000 BTU/h,
(e) R is the thermal resistance, â—¦F per BTU/h,
(f) u is the furnace switch, = 1 if the furnace is on and = 0 if the furnace
is off.
It is measured that, with the outside temperature at 32â—¦F and the house at 60â—¦F,
the furnace raises the temperature 2â—¦F in six min (0.1 h). With the furnace
off, the house temperature falls 2â—¦F in 40 min. What are the values of C and
R for the house?