Final answer:
Without specific geometry data of the cooling tower, numerical values for its volume and height cannot be accurately determined. Theoretical considerations suggest that using evaporation in cooling towers is much more efficient than simply heating the air to dissipate the waste heat.
Step-by-step explanation:
The volume of the cooling tower can be determined by dividing the mass flow rate of the air by the air density. The air density can be calculated using the ideal gas law and the given dry-bulb and wet-bulb temperatures:
Air density = (air mass flow rate per unit cross-sectional area) / (cross-sectional area) = malA / (πr^2)
Once you have the volume of the cooling tower, you can calculate its height by dividing the volume by the cross-sectional area:
Height = Volume / (cross-sectional area)
To determine the volume and height of the cooling tower, one would need additional geometry-specific data such as the cross-sectional area or the cooling tower's diameter. However, using the data given for the mass transfer coefficient-surface area product hDAv = 123 lbm/hr-ft³, and the air mass flow rate per unit cross-sectional area of the cooling tower malA = 1800 lbm/hr-ft³, we can discuss some theoretical aspects.
When dealing with such large volumes of air—equivalent to 12 million cubic feet of air per second—heating the air by 5°C for dissipation might not be efficient. Instead, these systems typically use evaporation to remove heat, which is more effective as it results in a much larger heat transfer than simply raising the temperature of the air.
Without specific measurements or further data about the particular design of the cooling tower, numerical values for volume and height cannot accurately be determined. For detailed calculations in a real-world scenario, an engineer would refer to specific design documents and carry out calculations based on the known geometry and physical principles governing cooling towers.