how many btu's does it take to raise one pound of water at 32 degrees f to the boiling point at 14.7 psia and then to steam?
To calculate the number of BTUs (British Thermal Units) required to raise one pound of water from 32 degrees Fahrenheit to the boiling point and then to steam, we need to consider three processes:
1. Heating the water from 32°F to its boiling point (212°F at standard atmospheric pressure).
2. Vaporizing the water at its boiling point.
3. Heating the steam from the boiling point to the final state described (which is not specified in the question).
1. To calculate the energy required to heat the water from 32°F to the boiling point (212°F), we use the specific heat capacity of water. The specific heat capacity of water is approximately 1 BTU per pound per degree Fahrenheit. Therefore, the energy required for this step is:
Energy = (Temperature change in Fahrenheit) × (Mass of water) × (Specific heat capacity of water)
= (212°F - 32°F) × (1 lb) × (1 BTU/lb/°F)
2. To calculate the energy required to vaporize the water at its boiling point, we use the latent heat of vaporization for water. The latent heat of vaporization is the amount of heat energy required to change a substance from liquid to vapor at a constant temperature and pressure. For water, it is approximately 970.4 BTU per pound.
Energy = (Mass of water) × (Latent heat of vaporization for water)
= (1 lb) × (970.4 BTU/lb)
3. The question does not specify the final state of the steam, so we cannot calculate the energy required for this step without additional information.
Therefore, the total energy required to raise one pound of water from 32°F to the boiling point and then to steam is the sum of the energy calculated in steps 1 and 2.