The $\mathrm{C}-\mathrm{C}$ bond energy order in ethane, ethene and ethyne is

Bond length is inversely proportional to the number of bonds between two atoms and bond energy, with increase in the number of bonds between two atoms bond length decreases and bond energy increases. Hence the bond energy of Ethyne is more when compared to ethane and ethene.

Therefore C C− bond energy order in ethane (C -C), ethene (C=C) and ethyne (C$\equiv$C) is ethene < ethyne < ethane.