There are three main phases: solids, liquids, and gases. Solids molecules are closely packed in an organized, lattice structure, liquid molecules are more spread apart and more disorganized, and gas molecules are spread even farther apart from each other and are extremely disorganized. Each type of solid is made up of unique type of atoms. For example, magnesium metal is made up of magnesium atoms whereas copper metal is made up of copper atoms. Since they are made up of unique atoms, different types of solids have different interactions between atoms. Some have strong interactions whereas others have very weak interactions; therefore, the energy required to break these interaction and separate the atoms/molecules (melt) is different for each solid. 

Recall that entropy is the level of disorder in a system. As mentioned, solids are highly organized structures; therefore, they will have the lowest entropy.

Freezing the is process of converting a liquid to a solid. This question is asking about the freezing process of liquid nitrogen to solid nitrogen; therefore, the end product of the reaction is solid nitrogen. Recall that solids are more tightly packed. This means that the volume taken up by the molecules in solid is lower than in liquid; therefore, solids generally have a lower volume. Mass, on the other hand, depends on the number of molecules present. Phase changes do not alter the amount of molecules present. For example, the end product in this question (solid nitrogen) will have the same amount of molecules as its liquid counterpart; therefore, the mass doesn’t change when the phase changes.

Density is defined as follows.

Since its volume decreases and the mass stays the same, a solid will have a lower density than liquid. Note that water is an exception to this general rule, as solid ice has a lower density (higher volume) than the same mass of liquid water. This is due to the arrangement of its hydrogen bonds throughout its crystalline structure. 

The dimensions of the cubic container are  by  by  (cube has same length, height, and width); therefore, the volume of the cubic container is

Recall that  is the same as ; therefore, the container can contain  of volume. This means that all of the solid will fit into the container. Upon melting, the solid will expand and the volume will increase (as it becomes liquid). This means that the volume of the container will not be sufficient for the liquid and, consequently, lead to an overflow of the liquid.

Liquid is an intermediate phase, between solid and gas. Solids are characterized by tightly packed molecules in an organized manner whereas gases are characterized by greatly spread out molecules that are highly disordered; liquids lie somewhere in the middle. This means that they are more disordered than solids (more entropy) and less disordered than gases (less entropy).

The boiling point of a substance is always higher than the melting point; therefore, you always need higher energy to break the interactions between liquid molecules.

The key difference between a liquid and a gas is the distance between the molecules. Liquid molecules are closer together whereas gas molecules are spread apart. Intermolecular forces are the forces between adjacent molecules. Since they are highly spread apart, the gas molecules have lower intermolecular forces.

Hydrogen bonding occurs between water molecules. While intermolecular forces between molecules exist for most molecules, these forces are much weaker than the bond formed between a hydrogen from one molecule and an oxygen, fluorine, and/or nitrogen atom of another molecule. Since the molecules are held more tightly together, more energy is required to break those bonds. This results in a higher temperature required to boil water (boiling breaks bonds between molecules, and this causes the molecules to escape into the gas phase).  

Recall than an object floats on water if it has a lower density than water. A floating or submerged object in a liquid has a gravitational pull (downward force) equal to the buoyancy force (upward force). The force due to gravity (gravitational pull) depends only on the mass of the object. In this case, the object can never be submerged because the density of the solid cannot be changed (unless the phase of the object is changed). To submerge, the object has to be placed in a liquid with LOWER density.

The volume of fluid displaced depends on the volume occupied by the object in the liquid. When an object floats, only part of the object is inside the liquid. This means that only part of the object’s volume is occupied inside the liquid (lower volume of fluid displaced). If the object were to be submerged (in a different liquid), the entire volume of the object would be inside the liquid and there would be an increase in the volume of fluid displaced.

Viscosity is a measure of resistance to flow. A liquid with high viscosity is said to have strong forces between its layers, making it harder to flow whereas a liquid with low viscosity has weak forces between its layers, making it easier to flow. Viscosity is quantified by the coefficient of viscosity (higher the coefficient, higher the viscosity and higher the resistance to flow). The question states that fluid A has more trouble flowing; therefore, fluid A has higher coefficient of viscosity and stronger forces between layers.

Poiseuille’s principle quantifies the flow rate of a fluid through a pipe to numerous variables as follows.

where  is the flow rate,  is change in pressure,  is radius,  is viscosity, and  is length. We can see that viscosity and length terms are in the denominator; therefore, flow rate and these two terms are inversely related. This means that increasing viscosity and/or length of pipe will decrease the flow rate (and vice versa). Note that the radius has the biggest exponential factor; therefore, altering radius of the pipe will contribute to the biggest change in flow rate.

To solve this question, we need to use the continuity equation and Bernoulli’s equation. The continuity equation is as follows:

where  is flow rate,  is velocity, and  is the area. This equation states that that the flow rate of a fluid is the same, regardless of changes in velocity and area. The equation implies that as the area is increased (for example, ) the velocity () decreases to maintain a constant flow rate and vice versa. The question states that End A has the larger radius; therefore, the velocity is lower at End A.

Bernoulli’s equation is as follows

where  is pressure,  is density,  is velocity,  is acceleration due to gravity, and  is the height from ground. This equation implies that as velocity is increased on one side, the pressure decreases to compensate. Since we already determined that End B has the higher velocity, it will also have the lower pressure.