The Physics
Hypertextbook
Opus in profectus

# Energy and Entropy

## Problems

### practice

1. Write something.
2. Write something different.
3. Write something completely different.
4. Write something else.

### conceptual

1. Rank the following arrangements of things (α, β, γ) from lowest to highest entropy.
1. The materials needed to build a house are all present in a building supply warehouse.
2. The materials are assembled into a house.
3. The house is destroyed by a tornado.
2. Table sugar (sucrose) is the crystallized remains left behind when then juice pressed from sugarcane (a tropical grass) or sugar beet (a root vegetable) is allowed to evaporate.
1. Which has the higher entropy: sugar crystals or the juice used to produce it? Explain.
2. Does the production of sucrose violate the second law of thermodynamics? Explain.
3. Ice cubes are dropped into a room temperature beverage to improve its refreshing qualities.
1. What happens to the entropy of the ice? Why does this happen?
2. What happens to the entropy of the beverage? Why does this happen?
3. How do the changes described above compare? Why must it be this way?
4. Two exoplanets are identical in nearly every way. (Planets orbit our sun. Exoplanets orbit stars that aren't our sun.) Both are rocky bodies like the Earth, our Moon, Mercury, Venus, or Mars. Both have the same density, chemical composition, mass, and radius. Both orbit stars that are identical in every way. The only difference between these two bodies is their atmosphere. One has an atmosphere like the Earth. (You live on earth, so I won't describe its atmosphere.) The other has an atmosphere like Mercury or our Moon, which means it basically doesn't have an atmosphere. Which planet has the higher entropy? Explain your choice.
5. A temperature gradient can exist between the top and bottom of a large mass of a fluid like a lake, a portion of the oceans, or a portion of the atmosphere. (Hot on the top and cool on the bottom or cool on the top and hot on the bottom — it doesn't matter.) Sometimes this fluid will undergo spontaneous convection (hot fluid rises, cool fluid sinks) and sometimes it will stratify (the fluid settles into stagnant layers that refuse to move). Assuming the same temperature gradient…
1. Which situation (convection or stratification) has the higher initial entropy? Explain your choice.
2. Which situation (convection or stratification) increases entropy faster? Explain your choice.
6. I was told something like this by someone I otherwise respect. "I have an air conditioner in my office that isn't connected to an outside vent." I said, "No you don't." Which was met with the reply, "Wanna bet?" My answer was, "No, I know that I am right and you are wrong and this bet is too easy to take. I'd rather bet you on something where you had a chance of being right." How could I have been so supremely confident with my answer?