Final answer:
A cooling tower's cooling capacity is not a fixed number and depends on multiple variables, and a heat balance calculation is needed to determine this based on design specifications and system requirements.
Step-by-step explanation:
The quantity of water a cooling tower can cool depends on various factors, including the dimensions of the tower, the flow rate of water and air, and the specific heat exchange mechanisms in place. The problem specified does not provide enough information to accurately determine the number of gallons a counter-flow cooling tower cools.
However, if you are looking for an answer based on theoretical understanding or from a specific data provided, you will need to apply principles of thermodynamics and heat transfer. Cooling towers fundamentally operate on the principle of heat rejection to the atmosphere via evaporation and heat exchange.
When solving problems related to cooling towers in an engineering context, you would typically perform a heat balance calculation with given parameters such as inlet and outlet water temperatures, flow rates, and heat transfer coefficients. There is often not a fixed quantity of water they cool, rather it is determined by the system's requirements and the design specifications of the tower.