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Q1. [14 Points] A factory has a large office space that it would like to air condition during the summer. Rather than buying electricity to run an air conditioner they design a system which allows them to run an air conditioning system using process steam from the factory. The factories boiler supplies saturated steam at 10 bar to an ideal condenser where it is completely condensed. This condenser supplies heat to a Carnot hear engine which in turn supplies power to a refrigeration cycle with a COP of 2.5. The refrigeration cycle cools a flow of air from 25°C to 5°C. Both the heat engine and refrigerator reject heat to a constant temperature reservoir at 25°C. If 0.5 kg/s of steam is supplied to the condenser, determine: a) the rate of heat input to the Carnot heat engine (kW), [3 Points] b) the power supplied to the refrigeration cycle (kW), [3 Points] c) the mass flow rate of 5 °C air produced by the system (kg/s), [3 Points] d) the entropy generation rate for the entire system (kW/K). [4 Points] e) Does the system violate the second law? Explain. [1 Point] msteam = 0.5 kg/s Psteam = 10 bar Saturated Vapor mair = ? kg/s Tair,in = 25 °C Cp = 1.01 kJ/kgK Saturated Liquid Condenser QH, Engine Carnot W QL Heat Refrigerator COP = 2.5 Engine QL, Engine QH Tambient = 25°C Tair,out= 5 °C

          Q1. [14 Points] A factory has a large office space that it would like to air condition during the
summer. Rather than buying electricity to run an air conditioner they design a system which
allows them to run an air conditioning system using process steam from the factory. The
factories boiler supplies saturated steam at 10 bar to an ideal condenser where it is completely
condensed. This condenser supplies heat to a Carnot hear engine which in turn supplies power to
a refrigeration cycle with a COP of 2.5. The refrigeration cycle cools a flow of air from 25°C to
5°C. Both the heat engine and refrigerator reject heat to a constant temperature reservoir at
25°C. If 0.5 kg/s of steam is supplied to the condenser, determine:
a) the rate of heat input to the Carnot heat engine (kW),
[3 Points]
b) the power supplied to the refrigeration cycle (kW),
[3 Points]
c) the mass flow rate of 5 °C air produced by the system (kg/s),
[3 Points]
d) the entropy generation rate for the entire system (kW/K).
[4 Points]
e) Does the system violate the second law? Explain.
[1 Point]
m<sub>steam</sub> = 0.5 kg/s
P<sub>steam</sub> = 10 bar
Saturated Vapor
mair = ? kg/s
Tair,in = 25 °C
C<sub>p</sub> = 1.01 kJ/kgK
Saturated Liquid
Condenser
Q<sub>H, Engine</sub>
Carnot
W
Q<sub>L</sub>
Heat
Refrigerator
COP = 2.5
Engine
Q<sub>L, Engine</sub>
Q<sub>H</sub>
T<sub>ambient</sub> = 25°C
T<sub>air,out</sub>= 5 °C

Q1. [14 Points] A factory has a large office space that it would like to air condition during the
summer. Rather than buying electricity to run an air conditioner they design a system which
allows them to run an air conditioning system using process steam from the factory. The
factories boiler supplies saturated steam at 10 bar to an ideal condenser where it is completely
condensed. This condenser supplies heat to a Carnot hear engine which in turn supplies power to
a refrigeration cycle with a COP of 2.5. The refrigeration cycle cools a flow of air from 25°C to
5°C. Both the heat engine and refrigerator reject heat to a constant temperature reservoir at
25°C. If 0.5 kg/s of steam is supplied to the condenser, determine:
a) the rate of heat input to the Carnot heat engine (kW),
[3 Points]
b) the power supplied to the refrigeration cycle (kW),
[3 Points]
c) the mass flow rate of 5 °C air produced by the system (kg/s),
[3 Points]
d) the entropy generation rate for the entire system (kW/K).
[4 Points]
e) Does the system violate the second law? Explain.
[1 Point]
m<sub>steam</sub> = 0.5 kg/s
P<sub>steam</sub> = 10 bar
Saturated Vapor
mair = ? kg/s
Tair,in = 25 °C
C<sub>p</sub> = 1.01 kJ/kgK
Saturated Liquid
Condenser
Q<sub>H, Engine</sub>
Carnot
W
Q<sub>L</sub>
Heat
Refrigerator
COP = 2.5
Engine
Q<sub>L, Engine</sub>
Q<sub>H</sub>
T<sub>ambient</sub> = 25°C
T<sub>air,out</sub>= 5 °C

Added by Jessica J.

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