Compounds $1$ and $2$ were prepared, and the difference in their heats of combustion was found to be $17\mathrm{.}2k\frac{J}{m}ol.$

$($a$)$ Redraw compounds $1$ and $2$ showing chair conformations for the six membered rings. In each case, draw the lowest energy conformation for the compound.

$($b$)$ Identify which compound has the larger heat of combustion. Explain your reasoning.

$($Hint: to analyze this question, check the structure of trans$-$decalin and use it as a model$).$