Which energy value correctly compares heating for phase changes of water: vaporizing vs melting?

Which energy value correctly compares heating for phase changes of water: vaporizing vs melting?

• A. It takes less BTUs to vaporize water than to melt ice into water.
• B. It takes more BTUs to vaporize water than to melt ice into water.
• C. It takes the same BTUs to vaporize water as to melt ice into water.
• D. It takes more BTUs to heat water from 50 to 60 F than to vaporize water.

Answer: (B)

The key idea is how much energy is needed to overcome intermolecular forces during a phase change—the latent heat. Melting ice into water at 0°C requires the latent heat of fusion, which is about 334 kJ/kg (roughly 144 BTU per pound). Vaporizing water into steam at 100°C requires the latent heat of vaporization, which is about 2257 kJ/kg (roughly 970 BTU per pound). So per unit mass, vaporizing needs far more energy than melting. This makes sense because melting only loosens the rigid crystal structure of ice to form a more fluid liquid, while vaporization must completely separate liquid molecules into gaseous molecules and allow them to expand against atmospheric pressure. That extra separation and expansion demand a much larger energy input.

The key idea is how much energy is needed to overcome intermolecular forces during a phase change—the latent heat. Melting ice into water at 0°C requires the latent heat of fusion, which is about 334 kJ/kg (roughly 144 BTU per pound). Vaporizing water into steam at 100°C requires the latent heat of vaporization, which is about 2257 kJ/kg (roughly 970 BTU per pound). So per unit mass, vaporizing needs far more energy than melting.

This makes sense because melting only loosens the rigid crystal structure of ice to form a more fluid liquid, while vaporization must completely separate liquid molecules into gaseous molecules and allow them to expand against atmospheric pressure. That extra separation and expansion demand a much larger energy input.