Internal Energy During Phase Changes

[Physics Fern]

I know that phase changes, such as the melting of ice, occur at constant temperature. Doesn't this imply that the change in internal energy during the phase change is zero, since the temperature remains the same? I thought that in all isothermal processes this was the case, so that the First Law of Thermodynamics becomes:

dU = dQ + dW
0 = dQ + dW
dQ = -dW

However, according to my textbook solutions, dU is not zero. Am I misunderstanding something? Thanks in advance!

 

[Physics Fern]

A thought to add...
During melting does the internal energy increase, but the increase goes towards breaking chemical bonds, rather than increasing the temperature of the substance? So dU is nonzero after all, even though it is an isothermal process?

The way I'm thinking about it now is that dU = 0 is true for all isothermal processes, except for isothermal phase changes.

Thanks.

 

[Ygggdrasil]

No. For ideal gasses, internal energy is dependent only on temperature. For other phases of mater, where you have interactions between particles, the internal energy depends on temperature and other factors.

For the vaporization of water, here's the picture. In water, water molecules form a are interacting with each other, forming hydrogen bonds, breaking them and forming new hydrogen bonds with other water molecules. In the gas phase, however, the water molecules are isolated and do not interact with each other. Therefore, in order to go from the liquid phase to the gaseous phase, you must first break apart the intermolecular hydrogen bonds between water molecules. Therefore, when boiling water (or similarly when melting ice), the heat that flows into the material goes toward breaking these intermolecular bonds instead of increasing the kinetic energy (temperature) of the material.

 

[Physics Fern]

Ah, thank you Ygggdrasil. I don't know why I was treating water as an ideal gas