The correct order of heat of combustion for following alkadienes is:

For structural isomers or compounds sharing the exact same molecular formula, the heat of combustion is inversely proportional to the thermodynamic stability of the molecule:

$$\text{Heat of Combustion} \propto \frac{1}{\text{Stability}}$$

A more stable molecule sits at a lower potential energy level, thereby releasing less energy (heat) when completely burned into $$\text{CO}_2$$ and $$\text{H}_2\text{O}$$.

Factors Influencing Alkadiene Stability:

1. Conjugation: Conjugated dienes (alternating double-single-double bonds) are significantly more stable than isolated dienes due to continuous $$\pi$$-electron delocalization.
2. Steric Geometries (Cis vs. Trans): Trans-alkenes experience less steric hindrance than cis-alkenes, making the trans,trans-isomer more stable than cis,trans or cis,cis arrangements.

Evaluating the Alkadienes:

• Structure (a): Trans,Trans-Conjugated Diene

  This structure has maximum conjugation along with the most sterically favorable trans,trans geometry. Because it has the lowest internal potential energy, it is the most stable and releases the least heat of combustion.




• Structure (b): Cis,Trans-Conjugated Diene

  This structure maintains the stable conjugated network, but contains a less favorable cis-alkene alignment creating minor steric strain. It possesses intermediate stability and intermediate heat of combustion.




• Structure (c): Cis,Cis-Conjugated or Non-Conjugated / Sterically Strained Diene

  This configuration experiences severe steric hindrance due to the crowded cis,cis arrangement of groups. Being the least stable isomer, it sits at the highest potential energy level and releases the highest heat of combustion.

Conclusion:

Reversing the overall stability trend ($$\text{a} > \text{b} > \text{c}$$) gives the correct increasing order of heat of combustion:

$$\mathbf{(a) < (b) < (c)}$$

Answer: Option A — (a) < (b) < (c)