Why is a cis-1,3-disubstituted cyclohexane more stable thanits

trans isomer?

Explanation has been given below

Explanation:

In diaxial conformation of cis-1,3-disubstituted cyclohexane, 4 gauche-butane interactions along with syn-diaxial interaction are present. Hence it readily gets converted to diequitorial conformation where no such gauche-butane interaction is present In two possible conformations of trans-1,3-disubstituted cyclohexane, 2 gauche-butane interactions are present in each of them. Hence cis-1,3-disubstituted cyclohexane exists almost exclusively in diequitorial form. But trans-1,3-disubstituted cyclohexane has no such option. Trans-1,3-disubstituted cyclohexane experiences gauche butane interaction in each of the two conformations. Therefore cis-1,3-disubstituted cyclohexane is more stable than trans conformation