If 1000 BTUs are removed from 100 lb of water at a temperature of 55 degrees Fahrenheit, what is the final water temperature?

To determine the final temperature of the water after removing 1000 BTUs, we can use the specific heat formula and some key concepts about the heat capacity of water.

The specific heat of water is approximately 1 BTU/lb°F, which means it takes 1 BTU to raise or lower the temperature of 1 pound of water by 1 degree Fahrenheit. If we have 100 pounds of water, it follows that the total quantity of heat capacity is 100 BTUs per degree Fahrenheit.

When 1000 BTUs are removed, we can calculate how much the temperature of the water changes. The temperature change (( \Delta T )) can be calculated as follows:

[

\Delta T = \frac{\text{Heat removed (in BTUs)}}{\text{Mass of water (in pounds)} \times \text{Specific heat of water (in BTU/lb°F)}}

]

Substituting the known values:

[

\Delta T = \frac{1000 \text{ BTUs}}{100 \text{ lb} \times 1 \text{ BTU/lb°F}} = \frac{1000}{100} = 10°F

]

Therefore,