(gas phase), a liquid and vapor phase of the same substance in equilibrium are actually in dynamic equilibrium, in which molecules in the gas phase are combining and condensing to form liquid, and molecules in the liquid phase are evaporating to form gas. The rates of these processes are the same, so the total proportions in the two phases remain constant.
When the water vapour condenses(say on your skin) it gives off kinetic energy.
So my answers is correct. It because there is small liquid droplets in the air. You know 100% humidity is feels very wet although it doesn't have to rain.
I always find the term vapour a bit "nebulous" (Har Har!)
Water is liquid or gas, "vapour" I consider is a water mist, the visible stuff from the kettle spout where the steam (invisible) condenses.
These are the droplets in the air, which might be warm, but are not about to give up latent heat to anything because they don't have any - they gave it up to the air already.
What gives up most of the heat is the "dry steam"
The balance between the gas and liquid phases is termed the dryness fraction and is indeed an equilibrium in a steady state system. There is "dry steam" in the air most of the time in temperate climates. without it you have a humidity of 0%.
You put a cold hand into warm humid air, if it's at 100% humidity you might see vapour (water mist) in the air. If it's less that 100% you won't.
Some of the gaseous water will condense on your skin (that is the dampness in the air) releasing latent heat until the temperature equilibrium is reestablished.
The humidity in the air locally will have dropped a bit as a result of the water condensing.
As a result the "vapour pressure" (misleading term!) will drop, and water molecules will be induced to come in from outside trying to equalise the partial pressure of water in the air.
Back to the original question:
Sorry Fudgeit2K, its kinda badly worded.
If I read you right, two boxes, differing humidities, same amount of heat energy applied to each. lower humidity will get warmer because there is not as big a mass of water in the box to absorb heat.
Faster? I'm not sure about the physics of that, you might think that it would get warm faster because there is less mass to heat.
But there's the same volume to heat and if the heat source is convective and the efficiency with which heat is transferred is the same at both humidities then it might take much the same time.
However, I suspect that higher humidity will improve heat transfer, given the higher heat capacity of water than air.