What is the heat flow in a 12 hour period through a single glass pane window looking into your backyard that is 4ft by 5 feet. The pane is 0.125 inches thick. It is summertime and the outside temperature is 85 deg F, and you are keeping the house a nice cool 75 deg F.

To solve this problem, we need to use the formula for heat flow (Q) through a plane wall, which is given by:

Q = kA(T1-T2)*t/d

where:

• k is the thermal conductivity of the material (for glass, it's approximately 0.84 W/mK),
• A is the area of the window,
• T1 and T2 are the temperatures on the two sides of the window,
• t is the time period for which we are calculating the heat flow, and
• d is the thickness of the window.

First, we need to convert all our measurements to SI units.

The area of the window (A) is 4ft by 5ft, which is 20 square feet. Converting to square meters, we get approximately 1.86 m^2.

The thickness of the window (d) is 0.125 inches. Converting to meters, we get approximately 0.003175 m.

The temperatures (T1 and T2) are given in Fahrenheit. Converting to Celsius, we get approximately 29.44°C (85°F) and 23.89°C (75°F). However, we need these temperatures in Kelvin for our calculation. So, we add 273.15 to each to get 302.59 K and 297.04 K.

The time period (t) is 12 hours. Converting to seconds (since our thermal conductivity is in W/mK), we get 43,200 seconds.

Now we can plug these values into our formula:

Q = 0.84 W/mK * 1.86 m^2 * (302.59 K - 297.04 K) * 43,200 s / 0.003175 m

Solving this, we get approximately 2,160,000 Joules or 2.16 MJ. This is the amount of heat that would flow through the window over a 12 hour period.