Why is the second Ionisation Enthalpy of alkali metals lower than the first, due to increased nuclear charge shouldn't it be harder to pull a second electron from it's orbit? 

Dear Student,

Lets write the equation representation for second ionizations energy to have comparison with first ionizations energy as below,

$X^{+}\left(g\right) \to X^{2+}\left(g\right) + e^{-}$

Let we consider an example of sodium for making the concept simpler, the sodium metal in initial it loses (or) shares one electron to a noble state hence the first ionisation energy is small as it loses electron by producing heat. If we need it lose another electron then more energy must have to be fed to make it lose second electron hence the ionisation of second one is high on comparing with first one. In general the forced one needs more energy for detaching /  losing electrons.

Regards.