| Description | Energy engineers frequently calculate the equation of state for gases. The Python example below is an example of calculating the value of an unknown variable using the ideal equation of state and the Van der waals equation of state. Ideal equation of state P = 0.082*T/V Van Der Waals equation of state P = (0.082 * T) / (V - b) - a / V^2
a = (27 * 0.082^2 * Tc^2) / (64 * Pc)
b = (0.082 * Tc) / (8 * Pc)
Python code of equation of state
import numpy as np
def eos(p, v, t, pc, tc, EOS, PVT):
delta = 99999;
delta_result = 99999;
if EOS == "Ideal":
if (PVT == 'P'):
p = 0.082 * t / v
result = p
elif PVT == 'V':
v = 0.082 * t / p
result = v
elif PVT == 'T':
t = p * v / 0.082
result = t
elif EOS == "VanderWaals":
a = 27*(pow(0.082,2)*pow(tc,2))/(64*pc)
b = 0.082*tc/(8*pc)
if PVT == 'P':
p = (0.082*t)/(v-b)-a/pow(v,2)
result = p
elif PVT == 'V':
v = 0.082 * t / p
v_start = v*1-(v*0.5)
v_end = v*1+(v*0.5)
v_interval = v*1/2000
Iteration = np.arange(v_start, v_end, v_interval)
for v_temp in Iteration:
p1 = p
p2 = (0.082*t)/(v_temp-b)-a/pow(v_temp,2)
delta = abs(p1 - p2)
if (delta < delta_result):
delta_result = delta
v_result = v_temp
v_result = round(v_result*1000)/1000
result = v_result
elif PVT == 'T':
t = (p*1+a/pow(v,2))*(v-b)/0.082
result = t
else:
pass
return result
P = 10 # Pressure (P, atm) = 10
V = 2.403 # Volume/mole (V, L/gmol) = 2.403
T = 298.15 # Temperature (T, K) = 298.15
Pc = 45.80 # Critical Pressure (Pc, atm) = 45.80
Tc = 190.7 # Critical Temperature (Tc, K) = 190.7
print(eos(P, V, T, Pc, Tc, 'Ideal', 'P'))
print(eos(P, V, T, Pc, Tc, 'Ideal', 'V'))
print(eos(P, V, T, Pc, Tc, 'Ideal', 'T'))
print(eos(P, V, T, Pc, Tc, 'VanderWaals', 'P'))
print(eos(P, V, T, Pc, Tc, 'VanderWaals', 'V'))
print(eos(P, V, T, Pc, Tc, 'VanderWaals', 'T'))
When run the code, you will receive the following results.
10.174
2.445
293.049
9.968
2.395
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