Help with relative humidity

Nov 2019
3
0
Sweden
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
Namnlös.jpg
 
Oct 2017
577
297
Glasgow
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)
 
Nov 2019
3
0
Sweden
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?
 
Oct 2017
577
297
Glasgow
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
 
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Nov 2019
3
0
Sweden
After calculating I have m of water = 180 g, how can I include relative humidity in question a?