Water is pumped from one reservoir to another. The water level in the second reservoir is 30 feet above the water level in the first reservoir. What is the increase in specific potential energy (energy per unit mass) of one pound of water in BTU?
The correct answer and explanation is:
To find the increase in specific potential energy of one pound of water in BTU, we will use the formula for potential energy: PE=m⋅g⋅hPE = m \cdot g \cdot h
Where:
- PEPE is the potential energy,
- mm is the mass of the water (in pounds),
- gg is the acceleration due to gravity,
- hh is the height difference between the two reservoirs (in feet).
In this case:
- m=1m = 1 pound,
- h=30h = 30 feet (the height difference between the reservoirs),
- g=32.174 ft/s2g = 32.174 \, \text{ft/s}^2 (the acceleration due to gravity in feet per second squared).
The potential energy in foot-pounds is calculated by: PE=1 lb×32.174 ft/s2×30 ftPE = 1 \, \text{lb} \times 32.174 \, \text{ft/s}^2 \times 30 \, \text{ft} PE=965.22 foot-poundsPE = 965.22 \, \text{foot-pounds}
Now, to convert foot-pounds to BTU (British Thermal Units), use the conversion factor: 1 BTU=778.169 foot-pounds1 \, \text{BTU} = 778.169 \, \text{foot-pounds}
Thus, the potential energy in BTU is: PEBTU=965.22 foot-pounds778.169 foot-pounds per BTUPE_{\text{BTU}} = \frac{965.22 \, \text{foot-pounds}}{778.169 \, \text{foot-pounds per BTU}} PEBTU≈1.24 BTUPE_{\text{BTU}} \approx 1.24 \, \text{BTU}
Explanation:
The potential energy of water in a reservoir depends on the weight of the water and the height difference from the reference point. In this scenario, 1 pound of water is raised by 30 feet, and the energy stored due to this elevation is the potential energy. The result is calculated in foot-pounds, but to express the energy in BTU, we convert using the conversion factor. The final value of approximately 1.24 BTU represents the increase in specific potential energy per pound of water when moved 30 feet upwards.