Answer:
The length of tank is found to be 0.6 m or 600 mm
Explanation:
In order to determine the length, we need to find a volume for the tank.
For this purpose, we use ideal gas equation:
PV = nRT
n = no. of moles = m/M
Therefore,
PV = (m/M)(RT)
V = (mRT)/(MP)
where,
V = volume of air = volume of container
m = mass of air = 4.64 kg
R = General Gas Constant = 8.314 J/mol.k
T = temperature of air = 10°C + 273 = 283 K
M = molecular mass of air = 0.02897 kg/mol
P = Pressure of Air = 20 MPa = 20 x 10^6 N/m²
V = (4.64 kg)(8.314 J/mol.k)(283 k)/(0.02897 kg/mol)(20 x 10^6 N/m²)
V = 0.01884 m³
Now, the volume of cylindrical tank is given as:
V = 0.01884 m³ = π(Diameter/2)²(Length)
Length = (0.01884 m³)(4)/π(0.2 m)²
<u>Length = 0.6 m = 600 mm</u>
