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3.8: Pressurized Cylinder: Carbon dioxide

3.8: Pressurized Cylinder: Carbon dioxide#

Problem Statement:#

A \(10\:L\) cylinder filled with pressurized \(CO_2\) is sitting at a temperature of \(T=20^\circ C\) in atmospheric pressure. The pressure guage reads a pressure of \(P_g=5.5\:MPa\). Assuming ideal gas application,

a) calculate how much \(CO_2\) is stored in the cylinder

b) calculate how much \(CO_2\) would be left if the cylinder is depressurized to atmospheric pressure

c) calculate how long the cylinder will last if the valve is open to a flow rate of \(10\:L/min\) (note: the volume rate is based on atmospheric pressure and ambient temperature \(T=20^\circ C\))

CH3-Q8.jpg

Solution Approach for a)#

based on ideal gas assumption,

\(PV=m_aRT\)

so

\(m_a=PV/{RT}\)

#define variables
R = 188.9   #gas constant in J/kg.K
T = 20 + 273.15   #temperature in K
P_g = 5.5E+6   #guage pressure in Pa
P_a = 101.325E+3   #atmosphric pressure in Pa
V = 10E-3   #gas container volume in m3

P = P_g + P_a   #absolute pressure in Pa

m_a = P * V / (R * T)   #mass in kg

print('The amount of CO2 stored is:', f"{m_a:.3f}", 'kg')

The amount of CO2 stored is: 1.012 kg

Solution Approach for b)#

same path as in a) for a different pressure

\(P=P_{atmospheric}\)

P = P_a   #absolute pressure in Pa

m_b = P * V / (R * T)   #mass in kg

print('The amount of CO2 stored after depressurizing is:', f"{m_b:.3f}", 'kg')

The amount of CO2 stored after depressurizing is: 0.018 kg

Solution Approach for c)#

the volume flow-rate is to be converted into mass flow-rate using density

\(D=m/V=\dot m/\dot V\)

so

\(\dot m=D\dot V\)

for an ideal gas

\(PV=mRT\)

therefore

\(D=m/V=P/RT\)

then, the mass flow-rate is used to calculate how long the cylinder will last based on the initial and final mass of the cylinder

assuming a constant flow-rate

\(\dot m=m/t\)

so

\(t=m/\dot m\)

P = P_a   #absolute pressure used for volume flow-rate in Pa

D = P / (R * T)   #density of CO2 flow in kg/m3

V_dot = 10E-3   #volume flow-rate in m3/min

m_dot = D * V_dot   #mass flow-rate in kg/min

t = (m_a - m_b) / m_dot   #cylinder lasting time in min

print('The cylinder will last', f"{t:.1f}", 'min based on the flow-rate')

The cylinder will last 54.3 min based on the flow-rate
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