Intermediate Thermodynamics Assignment 8 — Gaseous Mixtures  
$\xi$ is a parameter related to your student ID, with $\xi_1$ corresponding to the last digit, $\xi_2$ to the last two digits, $\xi_3$ to the last three digits, etc. For instance, if your ID is 199225962, then $\xi_1=2$, $\xi_2=62$, $\xi_3=962$, $\xi_4=5962$, etc. Keep a copy of the assignment — the assignment will not be handed back to you. You must be capable of remembering the solutions you hand in.
Question #1
A fixed amount of air initially at $(25+\xi_1)^\circ$C, 1 atm, and 50% relative humidity is cooled at constant pressure to 10$^\circ$C. Determine whether condensation occurs. Evaluate the amount of water condensed (kg of water condensed per kg of dry air), or if there is no condensation determine the relative humidity at the final state. Validate your answers by using the psychrometric chart.
Question #2
An air stream at 34$^\circ$C with a wet-bulb temperature of 15$^\circ$C and a mass flow rate of 1 kg/s passes through an evaporative cooler until the temperature is 21$^\circ$C. It is then heated to 30$^\circ$C. Determine the amount of liquid water added in the first section if the liquid water temperature is of $(30-2\times\xi_1)^\circ$C. Also determine the heat added in the second section of the equipment.
Question #3
Ambient air from outside a store is to be conditioned (by cooling to saturation conditions, condensation, and reheating) from a temperature of 29$^\circ$C and 80% relative humidity to a final state of 21$^\circ$C and $(40-\xi_1)$% relative humidity. If the pressure remains constant at 1 bar, calculate the amount of water removed, the heat removed in the cooling process, and the heat added in the final step of the process.
Question #4
Moist air (with a mass flow rate of 90 kg/min) with a temperature of $22^\circ$C and a wet-bulb temperature of $9^\circ$C enters a steam-spray humidifier. Saturated water vapor at $110^\circ$C is injected into the mixture at a rate of $(53-4\times\xi_1)$ kg/hr. There is no heat transfer with the surroundings, and the pressure is constant throughout at 1 atm. Determine at the exit (i) the humidity ratio, and (ii) the temperature.
Question #5
In an air-conditioning process 50 m$^3$/min of outside air at 29$^\circ$C and 80% relative humidity are mixed adiabatically with 100 m$^3$/min of inside air initially at 20$^\circ$C and $(30+4\times \xi_1)$% relative humidity and exit as a single stream. The total pressure of each stream is 1 bar. Compute for the resultant mixture (i) the dry-bulb temperature, (ii) the wet-bulb temperature, (iii) the humidity ratio, (iv) the relative humidity.
Question #6
It is desired to cool 1300 kg/min of water from 40$^\circ$C to 26$^\circ$C using a cooling tower. The cooling tower receives 800 m$^3$/min of air at 1 bar with dry-bulb and wet-bulb temperatures of 29$^\circ$C and 21$^\circ$C, respectively. If the evaporation rate from the water stream is 1600 kg/hr, determine the temperature of the exit air stream.
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