## How Much Water Vapour Is In A Cubic Metre Of Air at A Given Temperature And Relative Humidity?

I needed to know this as if I knew the temperature and relative humidity in my bedroom, when I went to bed and got up, I could work out how much water vapour had transferred to or from the air during my sleep.

One of my friends at school is an expert on these sort of calculations for industrial clients.

He came round on Friday night and we discussed it through, but I don’t think I got more than a basic grasp.

The reason is that he works from charts, whereas all my working life, I’ve started with proven formulae and worked everything out from first principles. But then I trained as a Control Engineer.

A problem I had with the psychometric charts he uses, is that they are all in a measurement system, that is totally foreign to me – Imperial. This is because most of the publishers are across the pond and they still use units, I last used in my early teens. When I went to work at ICI in the late sixties, the company had metricated in 1955 or so.

At least after our meeting and discussion, I now know what I’m searching for.

I finally found this web page, which gives a table of saturated vapour density for water in air. Although, it’s an American web site, at least it gives this in gm/cu. m.

The web page gives the SVP in gm/cu. m. at various temperatures

- 0°C – 4.85
- 10°C – 9.4
- 15°C – 12.83
- 20°C – 17.3
- 25°C – 23
- 30°C – 30.4
- 37°C – 44
- 40°C – 51.1

As an illustration, suppose you have a temperature of 25°C and a relative humidity of 50%. I measure it on my Maplin meter.

At that temperature a cubic metre of water can hold 23 grams of water. But as the relative humidity is 50%, it is actually only holding 11.5 grams of water. As my bedroom is about five metres square and two and a half metres high, that means the room contains over 719 grams of water.

Now look at 30°C and the same relative humidity of 50%.

The same calculation gives 950 grams of water in the room.

So if with the central heating, the electric blanket and the fact that each person probably is equivalent to a one bar electric fire, your bedroom, about the same size as mine, goes from say 25°C to 30°C, the air will need another 230 grams of water to be in equilibrium, or in layman’s terms, happy with how it relates to everything.

So from where does the air get this water it needs?

You!

No wonder a lot of people go to bed with a night bucket, so they can replenish the fluid they’ve lost to the air.

That’s a really useful assessment – I, too, have been trying to understand the basics but all the material online seems to be from the States, and is in units such as pounds, inches, Fahrenheit … and I work in SI units. I was trying to find out if a small humidifier would be able to produce enough vapour to keep the RH in my 1 cubic metre grow-tent high enough. To raise the RH by 10% at 25 degrees centigrade only requires 2.3g of water vapour, and the humidifier can produce 30ml per hour (so 30g per hour). That tells me that it can take the the air to saturation in less than an hour, whatever the starting conditions. Good to know, and great to be able to work it out! This article really helped.

Comment by John A | July 27, 2020 |

I generally work in SI for real problems, but because a lot of my readers seem to prefer it, I work in a funny mixed system these days. But then a lot of the web sites, that I use to do calculations can convert units.

Glad I was able to help.

Comment by AnonW | July 27, 2020 |

Good approach, but assumption that 1bar electric fire =1 person is MILES out. Assume 1 bar fire = 1000 watts. A sleeping person is less than 100watts. ( A champion cyclist might produce 1000 watts for 30 seconds in a sprint finish!). Therefore ,divide your sums by 10.

Comment by graham crocker | April 18, 2021 |