The correct order of the magnitude of heat of hydrogenation (to the corresponding alkane) of (I) but-1-ene, (II) cis-but-2-ene, (III) trans-but-2-ene…

Heat of hydrogenation measures how much less stable the alkene is than the alkane, so the more stable the alkene, the smaller the value. Stability increases with the number of alkyl groups on the double bond (hyperconjugation): but-1-ene is monosubstituted, both but-2-enes are disubstituted and 2-methylbut-2-ene is trisubstituted. Between the but-2-enes, the cis isomer has steric (van der Waals) strain, so it is less stable than trans. Stability: IV > III > II > I, hence heat of hydrogenation I > II > III > IV (about $127,\ 120,\ 116,\ 113\ \mathrm{kJ\,mol^{-1}}$).