Answer:
523°C
Explanation:
Step 1:
Data obtained from the question.
Diameter (d) = 31.0 cm
Height (h) = 37.2 cm
Pressure (P) = 5.90 MPa
Mass of ClF5 = 3.27 kg
Temperature (T) =?
Step 2:
Determination of the volume of the stainless-steel cylinder.
Volume of cylinder = πr^2h = π/4d^2h
V = π/4 x (31)^2 x 37.2
V = 28077.36 cm3
Converting the volume to L, we have:
1 cm3 = 0.001 L
Therefore, 28077.36 cm3 = 28077.36 x 0.001 = 28.07736 L
Step 3:
Conversion of 5.90 MPa to atm.
1 MPa = 9.869 atm
Therefore, 5.90 MPa = 5.90 x 9.869
= 58.2271 atm
Step 4:
Determination of the number of mole of chiorine pentafluoride gas (ClF5). This is illustrated below:
Molar Mass of ClF5 = 35.5 + (19x5) = 35.5 + 95 = 130.5g/mol
Mass of ClF5 = 3.27kg =3.27x10000
Mass of ClF5 = 3270g
Number of mole = Mass /Molar Mass
Number of mole of ClF5 = 3270/130.5
Number of mole of ClF5 = 25.057 moles
Step 5:
Determination of the temperature.
Applying the ideal gas equation
PV = nRT, the temperature T, can be obtained as follow:
P = 58.2271 atm
V = 28.07736 L
n = 25.057 moles
R (gas constant) = 0.082atm.L/Kmol
T=?
PV = nRT
Divide both side by nR
T = PV /nR
T = (58.2271x28.07736)/(25.057x0.082)
T = 795.68 K
Step 6:
Conversion of Kelvin temperature to celsius temperature.
°C = K - 273
K = 795.68 K
°C = 795.68 - 273
°C = 523°C
Therefore, the maximum safe operating temperature the engineer should recommend is 523°C
