Q:

How air humidity affects how much time is needed for heating the air?

In cold weathers it is suggested to put a humidifier since the air gets too dry. I wonder how the humidity affects how much time is needed to get the air at a temperature of 20 Celsius degrees? I mean suppose you have a cold room and you want to heat the air, Will the process be slower or faster in relation to variations in humidity?
Since the water tends to keep its temperature I feel the process will be slower with higher humidity, but I am not sure. 

A:

The heat capacity of humid air is approximately given by:
$$ C_p = 1.005 + 1.82H $$
where 1.005 kJ/kg°C is the heat capacity of dry air, 1.82 kJ/kg°C the heat capacity of water vapor, and H is the absolute humidity in kg water vapor per kg dry air in the mixture. So the specific heat capacity of humid air is greater than dry air and humid air will take more energy to heat by a given amount.
But the difference is quite small. I think 100% RH at 25C is only about 2% water, and if you need to heat the room the temperature, and therefore the water content, is presumably even lower. Taking the 2% water content only increases the specific heat by about 3.6%.

A:

Air has a specific heat capacity of slightly more than 1kJ/kgk at room temperature
So it takes a 1kW heater 1 second to heat 1kg (roughly 1 m^3)  of air 1 deg C
Fairly humid air (say 60% RH at 20C) will contain around 10g/m^3 of water vapour with a specific heat capacity of 1.8 kJ/kgk - so it takes almost twice as much energy (per unit mass) to heat the water in the air than the dry air itself.
But, only 10g in every 1kg of air is water vapour ( ie 1%) so you only have to do twice as much work to that 1%.
In other words - no you won't see any measurable difference.

