THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
8th Edition
ISBN: 9781307434316
Author: CENGEL
Publisher: INTER MCG
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Chapter 6.11, Problem 108P

(a)

To determine

The actual coefficient of performance of the refrigerator.

(a)

Expert Solution
Check Mark

Answer to Problem 108P

The actual coefficient of performance of the refrigerator is 4.33.

Explanation of Solution

Write the formula to calculate the mass flow rate of a refrigerant (m˙R).

m˙R=v˙1v1 (I)

Here, volume flow rate at inlet 1 is v˙1.

Write the formula to calculate the power consumption of the compressor (W˙in).

W˙in=m˙R(h2h1) (II)

Write the formula to calculate the refrigeration load (Q˙L).

Q˙L=Q˙heat+Q˙equipment (III)

Here, heating load rate is Q˙heat and other equipment load rate is Q˙equipment.

Write the formula to calculate the actual coefficient of performance.

COPactual=Q˙LW˙in (IV)

Conclusion:

Refer Table A-12, “Saturated refrigerant-134a: Pressure table”, obtain the properties of refrigerant R-134a at initial pressure (P1) of 400 kPa and quality 1.

h1=255.61kJ/kgv1=0.05127m3/kg

Refer Table A-13, “Superheated refrigerant-134a”, obtain the properties of refrigerant R-134a at exit pressure (P2) of 1.2 MPa and temperature (T2) of 70°C.

h2=300.63kJ/kg

Substitute 0.05127m3/kg for v1 and 80L/min for v˙1 in Equation (I).

m˙R=80L/min0.05127m3/kg=(80L/min(1m31000L)(1min60s)0.05127m3/kg)=0.02601kg/s

Substitute 0.02601kg/s for m˙R, 255.61kJ/kg for h1, and 300.63kJ/kg for h2 in Equation (II).

W˙in=0.02601kg/s(300.63kJ/kg255.61kJ/kg)=1.171kW

Substitute 250kJ/min for Q˙heat and 0.9 kW for Q˙equipment in Equation (III).

Q˙L=250kJ/min+0.9kW=250kJ/min(1min60s)+0.9kW=5.067kW

Substitute 1.171kW for W˙in and 5.067 kW for Q˙L in Equation (IV).

COPactual=5.067kW1.171kW=4.33

Thus, the actual coefficient of performance of the refrigerator is 4.33.

(b)

To determine

The maximum coefficient of performance of a reversible refrigerator.

(b)

Expert Solution
Check Mark

Answer to Problem 108P

The maximum coefficient of performance of a reversible refrigerator is 26.91.

Explanation of Solution

Write the formula to calculate the maximum coefficient of performance of a reversible refrigerator.

COPmax=1THTL1 (V)

Here, absolute temperature of high and low temperature reservoir is THandTL respectively.

Conclusion:

Convert the unit of temperature TL from °CtoK.

TL=23°C=(23+273)K=296K

Convert the unit of temperature TH from °CtoK.

TH=34°C=(34+273)K=307K

Substitute 296 K for TL and 307 K for TH in Equation (V).

COPmax=1307K296K1=26.91

Thus, the maximum coefficient of performance of a reversible refrigerator is 26.91.

(c)

To determine

The minimum volume flow rate at the compressor inlet.

(c)

Expert Solution
Check Mark

Answer to Problem 108P

The minimum volume flow rate at the compressor inlet is 12.9L/min.

Explanation of Solution

Write the formula to calculate the minimum power input to the condenser for the same refrigeration load (W˙in,min).

W˙in,min=Q˙LCOPmax (VI)

Write the formula to calculate the minimum mass flow rate (m˙R,min).

m˙R,min=W˙in,minh2h1 (VII)

Write the formula to calculate the minimum volume flow rate at the compressor inlet.(v˙min,1).

v˙min,1=m˙R,minv1 (VIII)

Conclusion:

Substitute 26.91 for COPmax and 5.067 kW for Q˙L in Equation (VI).

W˙in,min=5.067kW26.91=0.1883kW

Substitute 0.1883kW for W˙in,min, 255.61kJ/kg for h1, and 300.63kJ/kg for h2 in Equation (VII).

m˙R,min=0.1883kW300.63kJ/kg255.61kJ/kg=0.004182kg/s

Substitute 0.004182kg/s for m˙R,min and 0.05127m3/kg for v1 in Equation (VIII).

v˙min,1=(0.004182kg/s)(0.05127m3/kg)=0.0002144m3/s=12.9L/min

Thus, the minimum volume flow rate at the compressor inlet is 12.9L/min.

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Chapter 6 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

Ch. 6.11 - Does a heat engine that has a thermal efficiency...Ch. 6.11 - In the absence of any friction and other...Ch. 6.11 - Are the efficiencies of all the work-producing...Ch. 6.11 - Consider a pan of water being heated (a) by...Ch. 6.11 - Prob. 15PCh. 6.11 - Prob. 16PCh. 6.11 - A heat engine has a heat input of 3 104 Btu/h and...Ch. 6.11 - Prob. 18PCh. 6.11 - A 600-MW steam power plant, which is cooled by a...Ch. 6.11 - Prob. 20PCh. 6.11 - A heat engine with a thermal efficiency of 45...Ch. 6.11 - A steam power plant with a power output of 150 MW...Ch. 6.11 - An automobile engine consumes fuel at a rate of 22...Ch. 6.11 - Prob. 24PCh. 6.11 - Prob. 25PCh. 6.11 - A coal-burning steam power plant produces a net...Ch. 6.11 - An Ocean Thermal Energy Conversion (OTEC) power...Ch. 6.11 - What is the difference between a refrigerator and...Ch. 6.11 - Prob. 29PCh. 6.11 - In a refrigerator, heat is transferred from a...Ch. 6.11 - A heat pump is a device that absorbs energy from...Ch. 6.11 - Define the coefficient of performance of a...Ch. 6.11 - Define the coefficient of performance of a heat...Ch. 6.11 - Prob. 34PCh. 6.11 - A refrigerator has a COP of 1.5. That is, the...Ch. 6.11 - What is the Clausius expression of the second law...Ch. 6.11 - Show that the KelvinPlanck and the Clausius...Ch. 6.11 - Prob. 38PCh. 6.11 - Determine the COP of a heat pump that supplies...Ch. 6.11 - Prob. 40PCh. 6.11 - Prob. 41PCh. 6.11 - 6–42 An air conditioner removes heat steadily from...Ch. 6.11 - 6–43 A food department is kept at –12°C by a...Ch. 6.11 - A household refrigerator that has a power input of...Ch. 6.11 - When a man returns to his well-sealed house on a...Ch. 6.11 - Prob. 47PCh. 6.11 - Prob. 48PCh. 6.11 - 6–49 A heat pump is used to maintain a house at a...Ch. 6.11 - Prob. 50PCh. 6.11 - A household refrigerator runs one-fourth of the...Ch. 6.11 - Prob. 52PCh. 6.11 - Consider an office room that is being cooled...Ch. 6.11 - Prob. 54PCh. 6.11 - Refrigerant-134a enters the condenser of a...Ch. 6.11 - An inventor claims to have developed a resistance...Ch. 6.11 - Prob. 57PCh. 6.11 - A cold canned drink is left in a warmer room where...Ch. 6.11 - A block slides down an inclined plane with...Ch. 6.11 - Prob. 60PCh. 6.11 - Show that processes that use work for mixing are...Ch. 6.11 - Why does a nonquasi-equilibrium compression...Ch. 6.11 - Prob. 63PCh. 6.11 - Prob. 64PCh. 6.11 - Prob. 65PCh. 6.11 - Why are engineers interested in reversible...Ch. 6.11 - What are the four processes that make up the...Ch. 6.11 - Prob. 68PCh. 6.11 - Prob. 69PCh. 6.11 - Prob. 70PCh. 6.11 - Somebody claims to have developed a new reversible...Ch. 6.11 - Is there any way to increase the efficiency of a...Ch. 6.11 - Consider two actual power plants operating with...Ch. 6.11 - Prob. 74PCh. 6.11 - Prob. 75PCh. 6.11 - 6–76 A Carnot heat engine receives 650 kJ of heat...Ch. 6.11 - A Carnot heat engine operates between a source at...Ch. 6.11 - A heat engine operates between a source at 477C...Ch. 6.11 - Prob. 80PCh. 6.11 - Prob. 81PCh. 6.11 - In tropical climates, the water near the surface...Ch. 6.11 - 6–83 A well-established way of power generation...Ch. 6.11 - Prob. 84PCh. 6.11 - Prob. 85PCh. 6.11 - How can we increase the COP of a Carnot...Ch. 6.11 - In an effort to conserve energy in a heat-engine...Ch. 6.11 - Prob. 88PCh. 6.11 - Prob. 89PCh. 6.11 - 6–90 During an experiment conducted in a room at...Ch. 6.11 - Prob. 91PCh. 6.11 - An air-conditioning system operating on the...Ch. 6.11 - Prob. 93PCh. 6.11 - Prob. 94PCh. 6.11 - Prob. 95PCh. 6.11 - Prob. 96PCh. 6.11 - 6–97 A heat pump is used to maintain a house at...Ch. 6.11 - Prob. 98PCh. 6.11 - Prob. 99PCh. 6.11 - Prob. 100PCh. 6.11 - A commercial refrigerator with refrigerant-134a as...Ch. 6.11 - Prob. 102PCh. 6.11 - A heat pump is to be used for heating a house in...Ch. 6.11 - A Carnot heat pump is to be used to heat a house...Ch. 6.11 - A Carnot heat engine receives heat from a...Ch. 6.11 - Prob. 106PCh. 6.11 - Prob. 107PCh. 6.11 - Prob. 108PCh. 6.11 - Derive an expression for the COP of a completely...Ch. 6.11 - Prob. 110PCh. 6.11 - Prob. 111PCh. 6.11 - Prob. 112PCh. 6.11 - Prob. 113PCh. 6.11 - Someone proposes that the entire...Ch. 6.11 - Prob. 115PCh. 6.11 - Prob. 116PCh. 6.11 - Prob. 117PCh. 6.11 - It is often stated that the refrigerator door...Ch. 6.11 - Prob. 119RPCh. 6.11 - A Carnot heat pump is used to heat and maintain a...Ch. 6.11 - Prob. 121RPCh. 6.11 - Prob. 122RPCh. 6.11 - A refrigeration system uses a water-cooled...Ch. 6.11 - A heat pump with a COP of 2.8 is used to heat an...Ch. 6.11 - Prob. 125RPCh. 6.11 - Consider a Carnot refrigeration cycle executed in...Ch. 6.11 - Consider two Carnot heat engines operating in...Ch. 6.11 - Prob. 129RPCh. 6.11 - A heat engine operates between two reservoirs at...Ch. 6.11 - Prob. 132RPCh. 6.11 - An old gas turbine has an efficiency of 21 percent...Ch. 6.11 - Prob. 134RPCh. 6.11 - Prob. 135RPCh. 6.11 - Prob. 136RPCh. 6.11 - Prob. 137RPCh. 6.11 - Prob. 138RPCh. 6.11 - Prob. 139RPCh. 6.11 - A refrigeration system is to cool bread loaves...Ch. 6.11 - The drinking water needs of a production facility...Ch. 6.11 - Prob. 143RPCh. 6.11 - Prob. 145RPCh. 6.11 - Prob. 146RPCh. 6.11 - Prob. 147RPCh. 6.11 - Prob. 148RPCh. 6.11 - A heat pump with refrigerant-134a as the working...Ch. 6.11 - Prob. 150RPCh. 6.11 - Prob. 151RPCh. 6.11 - Prob. 153RPCh. 6.11 - Prob. 154RPCh. 6.11 - Prob. 155RPCh. 6.11 - A 2.4-m-high 200-m2 house is maintained at 22C by...Ch. 6.11 - Prob. 157FEPCh. 6.11 - Prob. 158FEPCh. 6.11 - A heat pump is absorbing heat from the cold...Ch. 6.11 - A heat engine cycle is executed with steam in the...Ch. 6.11 - A heat engine receives heat from a source at 1000C...Ch. 6.11 - Prob. 162FEPCh. 6.11 - A refrigeration cycle is executed with R-134a...Ch. 6.11 - A heat pump with a COP of 3.2 is used to heat a...Ch. 6.11 - A heat engine cycle is executed with steam in the...Ch. 6.11 - An air-conditioning system operating on the...Ch. 6.11 - Prob. 167FEPCh. 6.11 - Two Carnot heat engines are operating in series...Ch. 6.11 - Consider a Carnot refrigerator and a Carnot heat...Ch. 6.11 - A typical new household refrigerator consumes...Ch. 6.11 - A window air conditioner that consumes 1 kW of...
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