I have heard that using a humidifier in the winter can help you save money in heating costs. If this is true, I was curious about the physics behind why this is.
My thoughts were that since water has a very high specific heat, adding more water into the air would actually require you to use more energy to raise the temperature of the air the same amount.
Is it that if you use a humidifier, the perceived temperature is higher?(so maybe 67 degrees F with a humidifier would feel like 70 without, thus saving because you can keep the thermostat down?) If so, then how does humidity affect perceived temperature?
Or is it that this claim is wrong?
My background: I am a graduate student in combinatorics, a branch of math not very related to physics. I have seen undergraduate physics 1 & 2 in a formal setting, and enjoy learning about physics.