Which equation represents a spontaneous transmutation? ca(s) + 2h2o(ℓ) → ca(oh)2(aq) + h2(g)2kclo3(s) → 2kcl(s) + 3o2(g)?

Correct Ca(s) + 2H2O(ℓ) → Ca(OH)2(aq) + H2(g)

Reason:
A reaction (transmutation) is said to be spontaneous if it occurs on it's own, without any external stimulus. For spontaneous reaction, change in free energy (ΔG) is negative.

Among the given reactions, Ca(s) + 2H2O(ℓ) → Ca(OH)2(aq) + H2(g) occurs on its own with supplying external energy. Hence, it is a spontaneous reaction.  Further, it is an exothermic reaction. So during the reaction heat is given out by the system.

On other hand, reaction: 2KClO3(s) → 2KCl(s) + 3O2(g) is a decompostion reaction. For occurrence of reaction, heat has to be supplied to system. Hence, this reaction is non-spontaneous in nature. 

If the water vapor content stays the same and the temperature drops, then the relative humidity increases. its vise versa.if the water vapor content stats the same and the temperature rises, the relative humidity decreases. so, yes, i'd say that temperature and humidity have a strong relationship.