Heat Setting:
Because heat loss is such an important aspect of our life on this planet I would like you to apply your knowledge of basic heat transport to a problem which is potentially relevant to your life. This setting will necessarily be oversimplified but will hopefully illustrate the core ideas effectively. My inspiration comes from the tiny home movement in Portland and other places around the west as well as the PassiveHaus movement in Europe.
Imagine that you have a room that could be kept warm using only the heat of 1 human body when the temperature outside is -5 degrees C. A human body generates 100 W of heat energy under normal circumstances. There is a total of 2 m2 of triple glazed window in the room and the inside dimensions of the room are 4 m x 4 m x 3 m high. There is also a standard door (for the purposes of this exercise the door is .75 m wide and 2 m tall) We'll assume no door for now and the floors, walls, and ceiling are all equally insulated with standard fiberglass.
Like the refrigerator wall it is the interior insulating layer in the wall that does almost all the work. Here is a link to a table of thermal conductivities that you may find useful. This wiki page gives the thermal transmittance (this is the same keff we determined in lab which ignores the thickess of the wall) for various window types including our triple glazed window.
After you've worked out the intial problem you should consider how cold it can get outside if I have 100 W of lights running in my little room assuming that things remain at the same temperature inside.
How are you supposed to do this you ask? Let me offer some suggestions:
I) With the information provided you should be able to determine the thickness of the walls that will meet the design requirement. Don't forget that the window is a separate calculation from the walls and changes the surface area through which the heat is leaving. Assume initially that the door has the same thermal conductivity as the walls with no leaks.
II) How much air can you afford to have leak around the door and still maintain your temperature in the room? You will need your heat capacity ideas for this.
III) Now that you know the thickness of your walls you can determine how cold it can get outside if you have an extra 100 W of heat energy (the lights) adding to your room.
