Three thermometers describe a cooling tower, and the two differences you can make from them mean completely different things. Confusing them is the classic error on a commissioning sheet, so name them once, carefully.

Range: $\Delta T = T_h - T_c$, where $T_h$ is the hot water temperature arriving on the tower deck from the condenser, and $T_c$ is the cold water temperature leaving the basin. Both in °F here. Range is a fact about the water: how many degrees the tower actually removed. And here is the part that surprises people — range is set by the load and the flow, not by the tower. Put a bigger tower on the same chiller at the same pump flow and the range does not change.

Approach: $A = T_c - T_{wb}$, where $T_{wb}$ is the wet-bulb temperature of the air entering the louvres — the temperature a thermometer reads with a wet wick on it, which is the lowest temperature evaporation can ever reach. Approach is how far above that floor the basin water stopped. It is a fact about the tower: its size, its fill, its air flow, and how clean it is. A tower can be graded on approach alone.

Approach can never be zero — that would need infinite fill. Design approaches run 5 to 10 °F; an approach that has quietly grown from 7 to 12 over a summer is fouled fill or a slipping fan belt, and it will cost the chiller two or three percent of its efficiency per degree.

Then the heat itself: $Q = 500\,R\,\Delta T$, where $Q$ is the heat rejection rate in BTU per hour, $R$ is recirculation in gpm and $\Delta T$ is the range — never the approach. The 500 is not a fudge: it is 8.34 lb per gallon, times 60 minutes per hour, times 1 BTU per pound per °F for water. Learn it as that product and it survives any unit argument. In metric the same sentence reads $Q(\mathrm{kW}) = 4.18\,R(\mathrm{L/s})\,\Delta T(^\circ\mathrm{C})$, and it is the same physics wearing different trousers.