A typical electric air conditioner rated at 1.00 * 10^4 Btu/h (1 Btu = amount of energy required to raise the temperature of 1 lb of water by 1F). How much water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner?

I don't work in BTU (or BTU/hr) but I looked on the Internet and found that the heat of vaporization of water = 970 BTU/lb.

Therefore, mass water (lb) x heat vap = 1 x 10^4 BTU/hr
mass water * 970 BTU/lb = 1 x 10^4 BTU
mass water = 1 x 10^4/970 = ??
Check my thinking. Check my work.

easy

In order to determine how much water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner, we need to consider the amount of energy required to raise the temperature of the water by 1°F, and the amount of heat dissipated by the air conditioner.

Let's break down the problem step by step:

1. Convert the cooling capacity of the air conditioner from British thermal units per hour (Btu/h) to calories per hour. To do this, we need to know the conversion factor from Btu to calories. 1 Btu is approximately equal to 252.164 calories. So, we can calculate:

Cooling Capacity (in calories per hour) = 1.00 * 10^4 Btu/h * 252.164 cal/Btu.

2. Determine the amount of water that needs to be evaporated. To find this, we need to know the heat of vaporization of water. The heat of vaporization is the amount of heat energy required to convert 1 gram of water at boiling point into steam at the same temperature. The heat of vaporization of water is approximately 540 calories per gram.

Amount of Water (in grams) = Cooling Capacity (in calories per hour) / Heat of Vaporization (in calories per gram).

3. Finally, we need to convert the amount of water from grams to pounds. Since 1 pound is equal to approximately 453.592 grams, we can calculate:

Amount of Water (in pounds) = Amount of Water (in grams) / 453.592 g/lb.

Using these steps, we can now find how much water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner.