Calculate Inlet/Outlet Gas Relative Humidities

[missmaria]

Air is compressed to 10 atmospheres, cooled to 25 degrees C and passed through a bed of molecular sieve that has an initial moisture content of 8 lb water/100 lb sieve. the saturation vapor pressure of water at 25C is 24 mmHg. Assume M.W of air is 30 and the height of a transfer unit is 3 inches. How can i calculate the inlet and outlet gas relative humidities?

 

[hedenqvist]

You should use Fick's first laws and set up some mass balance for the mass transfer. Take the following source for some caluclated examples: http://www.composite-agency.com" . Regards, Hedenqvist

 

[oswaler]

To calculate the inlet and outlet gas relative humidities, we can use the following formula:

RH = (Pv/Pvs) * 100

Where:
RH = Relative humidity (in %)
Pv = Partial pressure of water vapor (in mmHg)
Pvs = Saturation vapor pressure of water at the given temperature (in mmHg)

For the inlet gas, we can use the following steps:

Step 1: Calculate the partial pressure of water vapor in the inlet gas.
Pv = (8 lb water/100 lb sieve) * (24 mmHg/1 lb water) = 1.92 mmHg

Step 2: Calculate the saturation vapor pressure of water at 25C.
Pvs = 24 mmHg

Step 3: Calculate the relative humidity of the inlet gas.
RH = (1.92 mmHg/24 mmHg) * 100 = 8%

Therefore, the inlet gas has a relative humidity of 8%.

For the outlet gas, we can use the following steps:

Step 1: Calculate the partial pressure of water vapor in the outlet gas.
Pv = (1.92 mmHg) * (30/10 atmospheres) = 5.76 mmHg

Step 2: Calculate the saturation vapor pressure of water at 25C.
Pvs = 24 mmHg

Step 3: Calculate the relative humidity of the outlet gas.
RH = (5.76 mmHg/24 mmHg) * 100 = 24%

Therefore, the outlet gas has a relative humidity of 24%.

It is also worth noting that the height of a transfer unit of 3 inches may affect the calculation of relative humidity, but without further information about the system, it is difficult to accurately account for this factor.