Perform a numerical estimate of the savings in heating energy for the residence modeled in §36.5.3 in Boston when the thermostat is turned off for eight hours, assuming that the outdoor temperature over the day varies sinusoidally with a mean temperature of 0 ^◦C and a maximum variation of ±5 ^◦C. You may assume the interior temperature set point is T_s = 18.3 ^◦C and that the thermostat is turned off over the coldest eight hours of the day.