Compare the boiling points of isobutane and 1-butyne Question: Compare between the boiling points of isobutane and 1-butyne


The answer to this question is given as 1-butyne has higher boiling point than isobutane.

My approach: I have been taught a few concepts (which I learnt for granted), in my organic chemistry class:

The carbon with a longer chain has a higher boiling point than its isomer with more branching or a shorter hydrocarbon chain. (Kindly correct me if I am wrong here and provide an explanation)

From here I decided that butyne will have a greater boiling point (though I made an incorrect assumption), and luckily my answer came out to be correct, but I am not convinced about the reason for it. Please help with the correct explanation for this question.
I have a proposition that since the electronegativity of $\mathrm{sp}$ hybridisation carbon is very high (only a little bit less than nitrogen), will it show hydrogen bonding? This justifies the given answer.
If it does not show hydrogen bonding, why so? All conditions are fulfilled, a highly electron deficient hydrogen is present and electrons are present in the $\pi$ bond between the carbons. Please help.
The boiling points of non-polar hydrocarbons are determined by the extent of van der Waals forces in between them. More specifically, molecules with a larger surface area have larger van der Waals forces of attraction between the molecules.

From the structures, it is obvious that but-1-yne has a larger surface area than isobutane, and hence has the higher boiling point.
Your idea of H-bonding in but-1-yne is plausible, according to this source1:

Quantum chemical calculations indicate hydrogen bond energies in the range $\pu{1–2.2 kcal mol^–1}$. Interconnected contacts such as $\ce{C#C–H ··· C#C–H ··· C#C–H}$ exhibit a pronounced cooperativity effect, with energy increases of $\approx \pu{0.5 kcal mol^–1}$ compared with isolated contacts.

However, while this bonding may be sufficient to explain a higher boiling point compared to isobutane, it is still a very weak bond compared to the H-bonds in hydrogen fluoride or water.
References:

Thomas Steiner, Evgeni B. Starikov, Ana M. Amado, José J. C. Teixeira-Dias, “Weak Hydrogen Bonding. Part 2. The Hydrogen Bonding Nature of Short $\ce{C–H ⋯\pi}$ Contacts: Crystallographic, Spectroscopic and Quantum Mechanical Studies of Some Terminal Alkynes.” J. Chem. Soc., Perkin Trans. 2 1995, (7), 1321–1326 (doi:10.1039/P29950001321).