If 10 pounds of refrigerant lose 20 BTUs of heat per pound in a water-cooled condenser, what is the temperature of the water leaving the condenser if it enters at 80°F?

To determine the temperature of the water leaving the condenser, we first need to calculate the total amount of heat removed from the refrigerant. Since the refrigerant loses 20 BTUs of heat per pound and there are 10 pounds of refrigerant, the total heat loss can be calculated as follows:

Total heat loss = 10 pounds × 20 BTUs/pound = 200 BTUs.

Next, we consider the water that enters the condenser at a starting temperature of 80°F. The heat absorbed by the water will equal the heat lost by the refrigerant, assuming no heat losses to the environment.

To find the final temperature of the water, we use the principle of heat transfer, knowing that:

Heat gained by water = Heat lost by refrigerant.

If we denote the specific heat capacity of water as 1 BTU/lb°F (standard value), we need to consider the mass flow rate of the water to determine how much the water temperature increases.

Assuming the water flow rate is sufficient to absorb this heat without significant temperature change in its mass, we calculate the temperature rise in the water from the absorbed heat:

If we let 'X' be the increase in temperature of the water, the relationship can be expressed as: