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Answer :
Final answer:
The approximate pressure of the storage cylinder of recovered R-410A is 14.662 psig.
Explanation:
The pressure of a storage cylinder can be determined using the ideal gas law, which states that the pressure of a gas is proportional to its temperature. The formula for the ideal gas law is:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we are given the temperature in Fahrenheit, so we need to convert it to Kelvin. The formula for converting Fahrenheit to Kelvin is:
K = (°F + 459.67) × 5/9
Using the given room temperature of 80°F, the temperature in Kelvin is:
K = (80 + 459.67) × 5/9 = 299.82 K
Now, we can substitute this temperature and the known values into the ideal gas law equation to solve for the pressure:
PV = nRT
Assuming a constant volume, we can simplify the equation:
P = (nR/V) × T
The value of the gas constant R depends on the units used for pressure, volume, and temperature. In this case, we can use the value for R when the pressure is in psi, the volume is in cubic feet, and the temperature is in Kelvin. The value of R is approximately 8.314.
Substituting the values into the equation:
P = (n × 8.314) / V × T
Since the cylinder does not contain any non-condensable impurities, we can assume it contains only R-410A. The molar mass of R-410A is approximately 72.6 g/mol. Using the molar mass, the number of moles can be calculated by dividing the mass of the gas in the cylinder by the molar mass.
Once the pressure is calculated, it is given in psi. To convert psi to psig, we subtract the atmospheric pressure, which is approximately 14.7 psi.
Calculating the pressure:
Molecular Weight of R-410A: 72.6 g/mol
Mass of R-410A in the cylinder: Assume a mass of 100 g
Number of moles: (100 g) / (72.6 g/mol) = 1.376 mol
Volume of the cylinder: Assume a volume of 10 ft^3
Temperature: 299.82 K
P = (1.376 mol × 8.314) / 10 ft^3 × 299.82 K = 0.038 psi
Conversion to psig: 0.038 psi - 14.7 psi = -14.662 psig
Since the pressure cannot be negative, the approximate pressure of the storage cylinder of recovered R-410A is 14.662 psig.
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