The thermodynamically most stable isomer in the given question is option (C), because both substituents occupy equatorial positions, minimizing 1,3‑diaxial steric interactions and overall ring strain.​

Introduction

In substituted cyclohexane, the thermodynamically most stable cyclohexane isomer is the conformer where bulky groups occupy equatorial positions to reduce 1,3‑diaxial repulsions and torsional strain. Understanding how to read chair conformations and distinguish axial versus equatorial substituents is essential for solving competitive‑exam questions that ask, “Which one of the following isomers is thermodynamically most stable?”.​

Core concept: axial vs equatorial and stability

• In a chair cyclohexane, each carbon bears one axial bond (approximately parallel to the ring axis, alternating up and down) and one equatorial bond (pointing roughly outward around the ring equator).​

• Substituents placed in axial positions suffer 1,3‑diaxial interactions with axial hydrogens (or other axial groups) on carbons 3 and 5, creating significant steric crowding.​

• Therefore, for mono‑ or disubstituted cyclohexanes, the most stable conformer is the one in which the larger and/or greater number of substituents are equatorial, making such a conformer lower in energy and hence thermodynamically preferred.​

In the given problem, the options represent different chair conformations (positional and conformational isomers) of the same substituted cyclohexane skeleton, differing in axial/equatorial orientation of the side chain on the ring.

Option‑wise explanation

Option (A): both substituents pseudo‑equatorial but gauche

In option (A), each substituent is drawn along the ring periphery, indicating predominantly equatorial‑type orientations on adjacent carbons of the chair.​​
However, the two groups are close and oriented such that the C–C bonds are gauche to each other, increasing steric repulsion between the side chains, so this conformer is not the lowest in energy among all options.​

Option (B): one equatorial, one axial (more axial strain)

Option (B) clearly shows one substituent oriented along the ring periphery (equatorial) and the other drawn nearly vertical (axial) on a neighboring carbon.​​
The axial substituent experiences 1,3‑diaxial interactions with axial hydrogens on the same face of the ring, raising the energy; hence option (B) is less stable than any conformer in which both substituents are equatorial.​

Option (C): both substituents equatorial (most stable)

In option (C), the longer vertical side chain is attached at a carbon where its carbon–carbon bond actually lies in the equatorial direction of that chair, while the second substituent on the neighboring carbon also points along the periphery, giving a diequatorial arrangement overall.​​
Because both groups are equatorial, 1,3‑diaxial interactions are minimized and the distance between substituents is maximized, so this conformer has the lowest steric strain and is therefore thermodynamically most stable, making option (C) the correct answer.​

Option (D): two axial‑type orientations (least stable)

In option (D), both substituents are oriented in directions corresponding to axial‑like bonds on adjacent carbons of the chair, one vertical and one leaning inward relative to the ring.​​
Having two axial substituents on the same side of the cyclohexane ring generates strong 1,3‑diaxial repulsions with multiple axial hydrogens (and between the substituents themselves), making this isomer the least stable of the four.​

Why option (C) is thermodynamically most stable

• The stability of substituted cyclohexanes correlates directly with the sum of “A‑values” for axial substituents; the conformer with the smallest total A‑value (fewest or no axial groups) is the most stable.​

• Among the four drawings, only option (C) can be interpreted as having both substituents equatorial, so it has zero axial substituents and hence the lowest overall A‑value and energy, leading to its predominance at equilibrium (thermodynamic control).​

Thus, option (C) is the thermodynamically most stable isomer in this cyclohexane chair‑conformation question.