A: The 4.5 rule of thumb assumes a standard air density of 0.075 lb/ft³, which is fine for conditioned indoor air but not for hot, humid outdoor air entering a cooling tower. In this problem, the entering air was hot and humid, so its specific volume is significantly higher than 0.075 — using the standard density would overstate the mass flow rate and give you the wrong heat transfer. When you're outside standard conditions, go back to the foundational equation using the actual specific volume from the psychrometric chart.

A: You did everything right up until the last step — the 4.5 rule embeds a standard air density that doesn't hold for hot humid air at the conditions given. You got all the way to the final calculation correctly; you just need to use the actual specific volume of the entering air to find the mass flow rate, then convert to CFM. That's the single fix.

A: Your overall strategy of equating the water-side heat transfer to the air-side heat transfer is exactly right. The problem is only on the air side: the 4.5 rule assumes a standard air density, but the entering air here is hot and humid, so you need to use the actual specific volume. Replace the 4.5 rule with ṁ × ΔH where ṁ = Q_air / ν, and you'll get the right answer.

A: The 500 × GPM × ΔT rule for water is very reliable because water density is close to constant across most operating ranges. The 4.5 × CFM × ΔH rule for air breaks down when air conditions deviate significantly from standard — specifically hot, humid, or high-altitude air. Use the air rule of thumb for normal HVAC supply/return conditions; go back to the foundational mass flow rate equation when you're dealing with outdoor air or unusual conditions.

A: This is the exact scenario where you need to step back from the rule of thumb — when the actual air state has a specific volume meaningfully different from 0.075 lb/ft³, the rule will lead you to the wrong answer choice. Whenever a problem involves outdoor air in unusual conditions (high humidity, high temperature, or high altitude), pull the specific volume directly from the psychrometric data and use the foundational equation. If both methods land on the same answer choice, the rule of thumb is fine; if they diverge, trust the specific volume.