# 11.2.3 Specific Heat and Latent Heat

Imagine we toss the coin into a furnace. If heat is supplied to the coin at a constant rate, its temperature would also rise at a constant rate. The heat supplied is used to increase the average KE of the jiggling atoms, manifesting in the rising temperature. In fact, the amount of heat required to raise the temperature of a unit mass of a substance by one unit of temperature is called the specific heat capacity c.

$Q=mc\Delta \theta$

There comes a point when the coin starts to melt. As the coin is melting, the temperature of the coin stays constant. (It resumes its ascent only after the coin is completely melted.) But heat is still being supplied at the same constant rate. So what happened to all the heat gained by the coin?

During the phase change, the heat supplied is used to increase the microscopic potential energy of the atoms in the coin. Since the average KE is constant, the temperature stays constant. But the increase in potential energy is evident because we can see the coin changing from solid phase to liquid phase. In fact, the amount of heat needed to convert a unit mass of a substance from solid to liquid form is called the specific latent heat of fusion Lf.

$Q=m{{L}_{f}}$

Likewise, the amount of heat needed to convert a unit mass of a substance from liquid to vapour form is called the specific latent heat of vaporization Lv.

$Q=m{{L}_{v}}$

Why (Ideal) Gas has Zero PE

A question for you; which has higher internal potential energy? 1 kg of water or 1 kg of ice?

A common misconception is that ice should have a higher PE since its molecules are more tightly bound. But do you remember that the GPE of two mutually attracting masses is negative? The closer the masses, the more negative the GPE! Intermolecular bonds are basically attractive electrical forces. The stronger the bond, the more negative the PE! For this reason, among the three states of matter, solids have the most negative PE, liquids have less negative PE, and (ideal) gases have zero PE.

Why is Latent Heat of Vaporisation so Large?

As discussed earlier, each atom in a solid lattice is rigidly bonded to its neighbouring atoms. Energy-wise, this means that the atoms in a solid lattice are each trapped in a very deep and narrow potential energy well. After melting, the potential energy wells become shallower and wider (thus allowing the atoms some mobility in the liquid). The latent heat of fusion is basically energy needed (1) to transfer the molecules from very deep potential energy wells to shallower wells[1].

What about boiling? After boiling, the molecules must be totally free from one another’s attractive forces. This means that there must be no potential energy wells at all in an ideal gas. So the latent heat of vaporization is used (2) to completely raise the molecules out of the potential energy wells[2] and (3) to do work against the atmospheric pressure (since the volume usually expands significantly after boiling). (2) and (3) are usually much larger than (1). Which is why the latent heat of vaporization is usually a lot larger than the latent heat of fusion.

Demonstration

Hand Boiler and Drinking Bird

Concept Test

1601

1607

1610

1617

[1] During exams, you can write this as “to weaken the intermolecular bonds”.

[2] During exams, you can write this as “to completely break down the intermolecular bonds”.