Question

A, B, and C are a solid liquid and gas.
Compare the Kinetic Energy of A and B


Compare the Potential Energy of A and B


Compare the Kinetic Energy of B and C

Answer 1

You haven't stated which letter is which state or whether they are all at the same temperature, so I’ll assume
- A = solid, B = liquid, C = gas
- all three are at the same temperature

Under those assumptions:

1) Kinetic energy of A vs B
- KE(A) = KE(B).
- Reason: average translational kinetic energy of particles depends only on temperature (〈KE〉 per particle = (3/2)kT for an ideal monoatomic gas); at the same T the particles in solid and liquid have the same average kinetic energy.

2) Potential energy of A vs B
- PE(A) < PE(B).
- Reason: in a solid particles are more tightly bound (lower potential energy); melting requires input of energy to overcome intermolecular attractions, so the liquid has higher potential energy.

3) Kinetic energy of B vs C
- KE(B) = KE(C).
- Reason: again, at the same temperature the average kinetic energy per particle is the same in liquid and gas.

If the temperatures differ, you cannot compare kinetic energies without those temperatures (higher T → higher mean KE).