When specific and latent heat are in close proximity?

I predicted that the specific heat and latent heat should be close to each other when the compressibility factor of the gas Z is > 1. In other words when there is more molecule to molecules of repulsion than attraction. This means when at phase change the molecules do need to do more work against molecular attraction than Z>1 and the latent heat of vaporization must be higher. When Z < 1, such gases like N2, O2, CH4, etc have more intermolecular forces to overcome and break them. This generates entropy. A part of the heat supplied goes to meet the entropy generation. That makes the heat of vaporization bigger than H2 and He, Z > 1 with intermolecular repulsion. It is interesting to note, helium gas has an almost equal amount of enthalpy of vaporization and sensible heat. He is an inert gas with Z >1, with very few intermolecular attractions and more repulsions between molecules.

I collected data as shown in the table and verified my thoughts. All data including my findings are summarized in the table below.

The table below has specific heat and latent heat of various gases. There is also a graph in the right corner showing the compressibility of different gases. I picked up five typical gases, Hydrogen, and helium which show Z > 1, and nitrogen, oxygen, and methane with Z<1

The specific heat and latent heat relationship at a glance

Latent heat is the heat that goes to break intermolecular bonds. Specific heat is the heat that goes to vibrate molecules. When a liquid gas is heated the liquid gas increases temperature by taking sensible heat. Its density decreases. Its volume increases. The entropy increases. When the liquid can no longer hold the load of entropy, the liquid phase changes into a gas phase by breaking intermolecular bonds. This is how and why phase changes happen. Phase change is nothing but an entropy-driven phenomenon

Now, here there is a catch. The phase change is not a free lunch. It needs the energy to increase volume against intermolecular forces. This energy is the enthalpy of vaporization. This energy primarily goes to meet the entropy requirements. The more the intermolecular attraction the more is the enthalpy of vaporization.

In cases, when there is more repulsion, Z > 1 between molecules, the enthalpy of vaporization becomes smaller and go near the H = Cpdt of the gas.

Key findings

Hydrogen

Sensible heat at boiling point 20.3k = 14.307 x 20.3= 290 KJ/KG

Latent heat of vaporization = 452 KJ/KG

Latent heat / Sensible heat = 452/290 = 1.56

Helium

Sensible heat at boiling point at 4.2 K = 4.2 x 5.1926 = 21.80 KJ/KG

Latent heat of vaporization = 20.9 KJ/KG

Latent heat / Sensible heat = 20.9/21.8 = 0.96

Nitrogen

Sensible heat at boiling point at 77.3 k = 1.039 x 77.3 = 80.3 KJ/KG

Latent heat of vaporization = 201 KJ/KG

Latent heat / Sensible heat = 201/80.3 = 2.50

Oxygen

Sensible heat at boiling point at 90.6 k= 0.658 x 90.6 = 59.6 KJ/KG

Latent heat of vaporization = 213 KJ/KG

Latent heat / Sensible heat = 213/59.6= 3.57

Methane

Sensible heat of methane CH4 at boiling point at 91.15K .7K = 2.2537 x 91.15 = 205.4 KJ/KG

Latent heat of vaporization = 511 KJ/KG

Latent heat / Sensible heat = 511/205 = 2.5

It may be noticed, the ratio of latent heat to sensible heat ratio is much smaller in two cases with H2 and He where Z>1 than other gases with Z<1.

Finally, just to summarize, when Z < 1, such gases like N2, O2, CH4, etc have more intermolecular forces to overcome and break them. This generates entropy. A part of the heat supplied goes to meet the entropy generation. That makes the heat of vaporization bigger than H2 and He, Z > 1 predominantly with intermolecular repulsion.

It is interesting to note, helium gas has an almost equal amount of enthalpy of vaporization and sensible heat. He is an inert gas with Z >1, with very few intermolecular attractions and more repulsions between molecules.