Why does a group of warmer atoms take up more volume than a group of cooler atoms?

Warmer atoms expand. There is also more movement. This is also explained when putting it into terms with solid vs. gas. In a solid, the atoms vibrate, but they can't move very far because there is not a lot of space between them. In a gas, on the other hand, the atoms are spread apart, and they move very fast. Putting it into context with water, the steam (gas) version is hot, and the ice cube (solid) version is cold. Which one moves more freely? The gas.

For cyclohexane compounds drawn in a chair conformation:   -axial bonds are vertical  -equatorial bonds are parallel to two bonds within the ring.  thus, as i assume the chair conformation is drawn:   -the x group is in an axial position, as are the five other vertical bonds.  -three axial bonds are on the top face of the ring  -the other three axial bonds are on the bottom face  the position of the second substituent on each ring carbon is equatorial.  gauche groups must be on an adjacent carbon such as carbon 6 and carbon 2, and also gauche groups are rotated by 60 degrees relative to each other.  drawing the newman projections for c1–c2 and c1–c6 aids in visualizing the groups that are gauche to the y group on c1.  click this link and watch some academic videos that may you more understand the topic 

The answer is a) carbon-12