Question 1186021: The volume of a 6 x 12-ft tank is 339.3 cu ft. It contains air at 200 psig and 85°F. How many 1-cu ft drums can be filled to 50 psig and 80°F if it is assumed that the air temperature in the tank remains at 85°F? The drums have been sitting around in the atmosphere which is at 14.7 psia and 80°F.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the number of drums that can be filled:
**1. Convert psig to psia:**
* Tank pressure: 200 psig + 14.7 psia = 214.7 psia
* Drum pressure: 50 psig + 14.7 psia = 64.7 psia
**2. Convert temperatures to absolute Rankine:**
* Tank temperature: 85°F + 460 = 545°R
* Drum temperature: 80°F + 460 = 540°R
**3. Use the ideal gas law to find the mass of air in the tank:**
The ideal gas law is PV = mRT, where:
* P = pressure
* V = volume
* m = mass
* R = specific gas constant for air (1716 ft-lbf/slug-°R)
* T = temperature
Rearranging to solve for mass: m = PV / RT
m = (214.7 psia * 144 in²/ft² * 339.3 ft³) / (1716 ft-lbf/slug-°R * 545 °R)
m ≈ 4.79 slugs
**4. Use the ideal gas law again to find the volume the air will occupy at drum conditions:**
We'll use the same formula, but this time we're solving for V: V = mRT / P
V = (4.79 slugs * 1716 ft-lbf/slug-°R * 540 °R) / (64.7 psia * 144 in²/ft²)
V ≈ 2216.7 ft³
**5. Calculate the number of drums that can be filled:**
Number of drums = Volume of air at drum conditions / Volume per drum
Number of drums = 2216.7 ft³ / 1 ft³/drum
Number of drums ≈ 2217 drums
**Therefore, approximately 2217 drums can be filled.**
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