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Please solve the problem using an atmospheric pressure of 85 kPa. Do not use a psychrometric chart but from first principles using formulae. I think you need to use steam tables:
In an air-conditioning unit 3.5 m^3/s of air at 27 degrees Celsius dry-bulb temperature, 50% relative humidity and standard atmospheric pressure enters the unit. The leaving condition of the air is 13 degrees Celsius dry-bulb temperature and 90 percent relative humidity. Using properties from the psychrometric chart:
a. Calculate the refrigerating capacity in kilowatts
b. Determine the rate of water removal from the air
c. Determine the mass of water vapor in 400 m^3 of air at 52 degrees Celsius and a relative humidity of 20% when the atmospheric pressure is 100 kPa and 85 kPa respectively.

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Problem 1:

a) Given: V_dot = 3.5 m3/s, T1 = 27C, phi_1 = 50%, T2 = 13C, phi_2 = 90%
p_0 = 85 kPa = 0.85 bar

Using Steam tables at saturation conditions, we find:

T = 27C = 300K --> p_sat = 0.03537 bar

We denote d = humidity content (kg water/kg dry air) which can be found using formula

d = 0.622*phi*p_sat/(p_0 - phi*p_sat) (1)

where phi = relative humidity, p_0 = ambient pressure

--> d = 0.622*0.5*0.03537/(0.85 - 0.5*0.03537) = 0.0132 kg water/kg dry air

We need now the air mass flow (M_dot):

M_dot = V_dot*rho = V_dot*p_0/(R*T) (2)

where rho = air density, computed by means of ideal gases ...

Solution Summary

This solution contains step-by-step calculations to determine the refrigerating capacity, rate of water removal and mass of water vapor using steam tables. All steps and formulas are included.