1. the relationships between ordered and disordered energies,
2. the statistical and probabilistic nature of thermodynamics,
3. the role of entropy in determining what is likely to happen,
4. the interplay of work, heat, and entropy.

1. When the outside air is hot and moist, your system's first goal is to extract the excess moisture. It does this by passing the air over a cold surface so that some of the moisture condenses and runs down a drain as liquid water. Why is this process inevitably going to (A) require electricity (or an equivalent source of ordered energy) and (B) going to require something to become hotter than the original outside air? [Note: ignore the possibility of tapping into the neighbor's air conditioning system or any other trick solution to your predicament. It's just your gallery and the outside air.]

2. Having chilled the air until it contains only the perfect amount of moisture, you want to reheat it to the ideal gallery temperature. You could use an electric heater or a woodstove, but you have another source of heat: the same device that was chilling the air in the first place. Instead of sending its heat outdoors, you can use some of that heat to warm the chilled air back to gallery temperature. But you have to be careful: if you use all of the heat that's released by the chiller, the gallery air will become hotter than the outdoor air! Why?

3. You arrange your climate control system so that as it pumps heat out of the new gallery air to chill it and dry it, part of that heat goes to the outdoor air and part to the indoor air. It turns out that sending some of this heat to the cooler, indoor air (rather than the hotter, outdoor air) makes the system more energy efficient--it uses less electricity! Why?

4. On one particular day, the outside air is exactly at gallery-air temperature. However, the outside air is too moist to use directly. So your climate control system chills it to extract some moisture and then reheats it back up to gallery temperature. When all this is done, you have drier air in the gallery and water running down the drain. Which system has more entropy: (1) a gallery full of outside air (moist but at the right temperature) or (2) a gallery full of dried air (drier and at the right temperature) plus the extracted water in the drain?

5. When the weather gets colder, the climate control system must begin warming the gallery air. Amazingly enough, it can do this relatively efficiently by transferring heat from the outside air into the gallery. However, your system must use electricity to carry out this heat transfer. Why won't the heat transfer occur naturally?

6. Instead of pumping heat into the gallery air from the outside air, you could simply put an electric space heater inside the gallery. A space heater turns electric energy directly into thermal energy. Why would operating a space heater consume more electric power than operating a heat pump?

7. When the air outside is very cold and dry, your climate control system must humidify the gallery air. It lets pure water evaporate into the air and raises the moisture content of that air. As this evaporation occurs, the temperature of the air drops somewhat because thermal energy is used to turn the liquid water into water vapor. But lowering the temperature of something usually means lowering its entropy. Why doesn't this process of mixing water and air to create slightly colder, moister air violate the second law of thermodynamics (the one requiring that overall entropy never decrease)?

8. Keeping the gallery door closed is important, so you install a sophisticated closing system that keeps the air exchange between inside and outside to a minimum. Why will such air exchanges always make your gallery consume extra electricity (and money)?