# Help with relative humidity

#### essi088

Hi,
Can somebody help me with this question please?

In humid air with a water content of 3 g / (kg dry air), liquid water is injected at a temperature of 30 ° C, after which the air temperature becomes 18 ° C and its relative humidity 50%. The total pressure is constant 1.013 bar and the mass of the dry air is 60 kg. Calculate:
a) the amount of water injected;
b) the air temperature before water is injected

#### benit13

The ideal gas law and the definitions of humidity and relative humidity can get you through this one.

The ideal gas law is this:
$$\displaystyle pV = nRT$$

p = total pressure (sum of partial pressure of dry air and water vapour; Pa)
V = volume (m3)
n = number of moles of air (sum of number of moles of dry air and water vapour; mol)
R = real gas constant
T = dry-bulb temperature (Kelvin)

Humidity:
$$\displaystyle W = \frac{m_{water}}{m_{dry-air}}$$

m = mass of constituent (kg)

Relative humidity:
$$\displaystyle \phi = \frac{p_v}{p_{sat}}$$

$$\displaystyle p_v$$ = partial water vapour pressure (Pa)
$$\displaystyle p_{sat}$$ = partial water vapour pressure of saturated air (Pa)

#### essi088

Thank you for your answer. I don't understand what W is in my question? And if I know the W is problem a) solved?

#### benit13

W is humidity (in kg water vapour per kg of dry air). The first value specified in your question, "water content", is humidity: W = 0.003

topsquark

#### essi088

After calculating I have m of water = 180 g, how can I include relative humidity in question a?