(For people who don’t want to hear the back-story, you can skip the first paragraph. Also moderators, this is not a homework question.)
One of my pet peeves is low indoor relative humidity. I have naturally dry skin and I am easily irritated by low relative humidity (I get many nose-bleeds, always have a dry throat, occasional hand-bleeding, etc.) and that is why I don’t like the climate in New England (and sometime in the future, may consider moving to a warmer and more humid climate). That’s why we have maximized the humidity setting on our heater at home so that even in the coldest winters we are able to maintain a 40-50% relative humidity (thus, I don’t have any issues). However, most public areas don’t seem to have this function , and I am pretty sure it is much less than 40-50% in those areas.
One thing that I found interesting is that on my Galaxy Nexus, there is an app in the Google Play store where you basically input a value for outdoor relative humidity and temperature and indoor temperature, and it gives you a reading for the expected relative humidity inside.
However, I am not sure if it is a legit app, and I was curious to know if there is a certain mathematical formula for this.
Basically, you are given the outdoor relative humidity and temperature and the indoor temperature, and you want to determine the indoor relative humidity; what is the formula to find this?
I can’t answer your question but I’m wondering why you don’t just get a cheap hygrometer? I have one that came with my humidifier and it lets me know when I should use it. They are as cheap as a couple of bucks.
It probably assumes that the absolute humidity is the same. If you take the outside air and heat it up to the indoor temperature, the actual amount of water vapor in the air does not change, but relative humidity goes down because relative humidity is a function of temperature.
Obviously, this assumption is invalid if you have a humidifier.
At any given air temperature, the air can hold a certain amount of water vapor before becoming saturated. The warmer air becomes, the more water vapor it can hold, and vice-versa.
If I know the relative humidity at a given air temperature, I can figure out the “dewpoint” for the amount of water vapor that’s currently in the air…the dewpoint is the temperature at which the relative humidity is at 100%.
Knowing the dewpoint of the cold outdoor air, I can figure out the relative humidity if I then heat up the air to a comfortable interior temperature. This assumes the same level of water vapor in the air (and, thus, the same dewpoint) when you move the air from outside to inside.
So, yes, it’s just a simple set of mathematical formulas, and yes, it’s accurate. (And, no, I don’t know the exact formulas off the top of my head; I’m only an amateur meteorologist. )
Note that the conversion to your interior relative humidity which I just described only works if you aren’t adding more water vapor to the air in your house via a humidifier, which you indicate you have.
The relationship between states of gas-vapor mixtures is described by psychrometry.
Your app is legitimate, with a couple of caveats - First, it assumes that the absolute humidity is the same inside and outside (i.e., there is no process that would dehumidify or humidify the air as it comes indoors). Second, unless you can specify your altitude, it probably assumes conditions at sea level. If you are not at sea level, there will be some error. A fancy app might be able to use location data to determine your altitude and make corrections.