To determine if the house is losing more or less heat than it is gaining from the sun through an east-facing window on a typical day in January, we need to calculate the rate of heat gain and the rate of heat loss, and compare them.
Heat gain from the sun through the window:
The solar heat gain through the window can be calculated using the following formula:
Q = A × SHGC × I
where Q is the rate of heat gain, A is the area of the window, SHGC is the solar heat gain coefficient, and I is the solar radiation intensity.
For a double-door-type window with double paned 3-mm-thick glasses and 6.4 mm of airspace, the SHGC is typically around 0.6. The solar radiation intensity depends on the angle of incidence of the sun's rays, which varies throughout the day and with the season. For simplicity, we can assume an average value of 500 W/m² for a typical winter day in Reno, Nevada.
Assuming the east-facing window has an area of 2 m², we can calculate the rate of heat gain through the window as:
Qgain = 2 × 0.6 × 500 = 600 W
Heat loss through the window:
The rate of heat loss through the window can be calculated using the following formula:
Q = U × A × ΔT
where Q is the rate of heat loss, U is the overall heat transfer coefficient, A is the area of the window, and ΔT is the temperature difference between the indoor and outdoor air.
For a double-door-type window with aluminum frames and spacers, the overall heat transfer coefficient is typically around 3.5 W/m²K. Assuming a temperature difference of 22°C - 10°C = 12°C, we can calculate the rate of heat loss through the window as:
Qloss = 3.5 × 2 × 12 = 84 W
Comparison:
Comparing the rate of heat gain and the rate of heat loss, we can see that the house is gaining more heat than it is losing through the east-facing window on a typical day in January in Reno, Nevada.
Qgain = 600 W > Qloss = 84 W
Therefore, the house is gaining more heat than it is losing from the sun through the east-facing window on a typical day in January.