9 A passive solar house has a thermal mass consisting of 20

9) A passive solar house has a thermal mass consisting of 20 tonnes of concrete. The houses energy loss rate is 120W/ °C. At the end of a sunny winter day, the entire house, including the thermal mass, is at 22°C. If the outdoor temperature is -10°C, how long after the Sun sets will it take the house’s temperature to drop by 1°C?

Solution

Concrete specific heat = 880 J/Kg.K

Heat loss by house in dropping 1 degree of temperature = msT = 20000x880x1=176x10⁵ J

House energy loss rate = 120W per degree of temperature difference = 120 x (22-(-10)) = 3840W

So total time taken to drop 1 degree of temperature = 176x10⁵ /3840 = 4583 Seconds =1hr 16minutes 23seconds