6.12: Second Law for a Refrigration Cycle#
Problem Statement#
A refrigration cycle works between a cold space at temperature
a) heat dissipated into heat sink
b) COP of the cycle
Assuming the heat absorbtion from the cold environment happens at
c) entropy generation (is this feasible?)
d) COP of the Carnot cycle (how does this compare?)
Assuming the cycle operates with a Carnot COP,
e) how much work is required for the same cooling load
f) how much heat is dissipated into the heat sink
g) entropy generation
Solution Approach for a)#
from the first law
#define inputs
Q_L = 50e+3 #heat absorbed from cool space in W
W = 10e+3 #cycle work input in W
Q_H = Q_L + W #heat dissipated into heat sink in W
print('The amount of heat dissipated into heat sink is:', f"{Q_H/1000:.1f}", 'kW')
The amount of heat dissipated into heat sink is: 60.0 kW
Solution Approach for b)#
for a refrigration cycle
COP = Q_L / W #COP of the cycle
print('The COP of the cycle is:', f"{COP:.1f}")
The COP of the cycle is: 5.0
Solution Approach for c)#
from the second law for a closed system
since the cycle is steady
therfore
#define variables
T_L = -20 + 273.15 #low temperature in K
T_H = 60 + 273.15 #high temperature in K
S_gen = -1 * (Q_L / T_L - Q_H / T_H) #negative sign for Q_H due to heat leaving the system
print('The entropy generation of the system is:', f"{S_gen:.1f}", 'W/K')
The entropy generation of the system is: -17.4 W/K
Solution Approach for d)#
COP_C = 1 / (T_H / T_L - 1)
print('The Carnot COP for the cycle is:', f"{COP_C:.1f}")
The Carnot COP for the cycle is: 3.2
Solution Approach for e)#
W = Q_L / COP_C
print('The work input for the refrigration cycle based on Carnot operation is:', f"{W/1000:.1f}", 'kW')
The work input for the refrigration cycle based on Carnot operation is: 15.8 kW
Solution Approach for f)#
from the first law
Q_H = Q_L + W
print('The heat dissipation based on Carnot operation is:', f"{Q_H/1000:.1f}", 'kW')
The heat dissipation based on Carnot operation is: 65.8 kW
Solution Approach for g)#
S_gen = -1 * (Q_L / T_L - Q_H / T_H) #negative sign for Q_H due to heat leaving the system
print('The entropy generation of the system based on Carnot COP is:', f"{S_gen:.1f}", 'W/K')
The entropy generation of the system based on Carnot COP is: -0.0 W/K