THERMODYNAMICS: ENG APPROACH LOOSELEAF
THERMODYNAMICS: ENG APPROACH LOOSELEAF
9th Edition
ISBN: 9781266084584
Author: CENGEL
Publisher: MCG
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Textbook Question
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Chapter 6.11, Problem 112P

A Carnot heat engine receives heat from a reservoir at 900°C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27°C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at −5°C and transfers it to the same ambient air at 27°C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

(a)

Expert Solution
Check Mark
To determine

The rate of heat removal from the refrigerated space.

Answer to Problem 112P

The rate of heat removal from the refrigerated space is 4982kJ/min_.

Explanation of Solution

Determine the highest thermal efficiency a heat engine between two specified temperature limits.

ηth,max=1TLTH (I)

Here, the temperature inside the refrigerator is TH, and the temperature outside the refrigerator is TL.

Determine the maximum power output of this heat engine.

W˙net=ηth×Q˙H (II)

Here, the rate of heat gain per unit degree is Q˙H.

Determine the coefficient of performance of the Carnot refrigerator depends on the temperature limits in the cycle.

COPR=1(TH/TL)1 (III)

Determine the rate of heat removal from the refrigerator space.

Q˙L,R=(COPR)×(W˙net) (IV)

Conclusion:

Substitute 27°C for TL and 900°C for TH in Equation (I).

ηth,max=1(27°C)(900°C)=1(27°C+273)(900°C+273)=10.25575=0.744

Substitute 0.744 for ηth,max and 800kJ/min for Q˙H in Equation (II).

W˙net=(0.744)(800kJ/min)=595.2kJ/min

Substitute 5°C for TL and 27°C for TH in Equation (III).

COPR=1((27°C)/(5°C))1=1((27°C+273)/(5°C+273))1=1(0.11940K)1=8.375

Substitute 8.375 for COPR and 595.2kJ/min for W˙net in Equation (IV).

Q˙L,R=(8.37)×(595.2kJ/min)=4981.8kJ/min

Thus, the rate of heat removal from the refrigerated space is 4982kJ/min_.

(b)

Expert Solution
Check Mark
To determine

The total rate of heat rejection to the ambient air.

Answer to Problem 112P

The total rate of heat rejection to the ambient air is 5782kJ/min_.

Explanation of Solution

Determine the total heat rejected by refrigerator.

Q˙H,R=W˙net+Q˙L (V)

Determine the total heat rejected by heat pump.

Q˙L,HE=W˙net+Q˙L (VI)

Determine the total heat rejected to ambient.

Q˙ambient=Q˙L,HE+Q˙H,R (VII)

Conclusion:

Substitute 800kJ/min for Q˙H,HE and 595.2kJ/min for W˙net in Equation (V).

Q˙L,HE=(800kJ/min)(595.2kJ/min)=204.8kJ/min

Substitute 4982kJ/min for Q˙L,R and 595.2kJ/min for W˙net in Equation (VI).

Q˙H,R=(4982kJ/min)+(595.2kJ/min)=5577.2kJ/min

Substitute 204.8kJ/min for Q˙L,HE and 5577.2kJ/min for Q˙H,R in Equation (VII).

Q˙ambient=(204.8kJ/min)+(5577.2kJ/min)=5782kJ/min

Thus, the total rate of heat rejection to the ambient air is 5782kJ/min_.

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Chapter 6 Solutions

THERMODYNAMICS: ENG APPROACH LOOSELEAF

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That is, the...Ch. 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 - What is the Clausius expression of the second law...Ch. 6.11 - Show that the KelvinPlanck and the Clausius...Ch. 6.11 - The coefficient of performance of a residential...Ch. 6.11 - A food freezer is to produce a 5-kW cooling...Ch. 6.11 - An automotive air conditioner produces a 1-kW...Ch. 6.11 - A food refrigerator is to provide a 15,000-kJ/h...Ch. 6.11 - Prob. 44PCh. 6.11 - Determine the COP of a heat pump that supplies...Ch. 6.11 - Prob. 46PCh. 6.11 - A heat pump with a COP of 1.4 is to produce a...Ch. 6.11 - An air conditioner removes heat steadily from 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 - Water enters an ice machine at 55F and leaves as...Ch. 6.11 - A refrigerator is used to cool water from 23 to 5C...Ch. 6.11 - A household refrigerator runs one-fourth of the...Ch. 6.11 - 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Prob. 78PCh. 6.11 - A thermodynamicist claims to have developed a heat...Ch. 6.11 - A heat engine is operating on a Carnot cycle and...Ch. 6.11 - A completely reversible heat engine operates with...Ch. 6.11 - An inventor claims to have developed a heat engine...Ch. 6.11 - A Carnot heat engine operates between a source at...Ch. 6.11 - A heat engine is operating on a Carnot cycle and...Ch. 6.11 - A heat engine operates between a source at 477C...Ch. 6.11 - An experimentalist claims that, based on his...Ch. 6.11 - In tropical climates, the water near the surface...Ch. 6.11 - Prob. 89PCh. 6.11 - Prob. 90PCh. 6.11 - Prob. 91PCh. 6.11 - Prob. 92PCh. 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. 95PCh. 6.11 - Prob. 96PCh. 6.11 - A thermodynamicist claims to have developed a heat...Ch. 6.11 - Determine the minimum work per unit of heat...Ch. 6.11 - Prob. 99PCh. 6.11 - An air-conditioning system operating on the...Ch. 6.11 - A heat pump operates on a Carnot heat pump cycle...Ch. 6.11 - An air-conditioning system is used to maintain a...Ch. 6.11 - A Carnot refrigerator absorbs heat from a space at...Ch. 6.11 - Prob. 104PCh. 6.11 - A Carnot refrigerator operates in a room in which...Ch. 6.11 - Prob. 106PCh. 6.11 - A commercial refrigerator with refrigerant-134a as...Ch. 6.11 - Prob. 108PCh. 6.11 - A heat pump is to be used for heating a house in...Ch. 6.11 - A completely reversible heat pump has a COP of 1.6...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. 113PCh. 6.11 - Derive an expression for the COP of a completely...Ch. 6.11 - Calculate and plot the COP of a completely...Ch. 6.11 - Prob. 116PCh. 6.11 - Prob. 117PCh. 6.11 - Prob. 118PCh. 6.11 - Someone proposes that the entire...Ch. 6.11 - Prob. 120PCh. 6.11 - Prob. 121PCh. 6.11 - Prob. 122PCh. 6.11 - It is commonly recommended that hot foods be...Ch. 6.11 - It is often stated that the refrigerator door...Ch. 6.11 - Prob. 125RPCh. 6.11 - Prob. 126RPCh. 6.11 - Prob. 127RPCh. 6.11 - A Carnot heat pump is used to heat and maintain a...Ch. 6.11 - A refrigeration system uses a water-cooled...Ch. 6.11 - A refrigeration system is to cool bread loaves...Ch. 6.11 - A heat pump with a COP of 2.8 is used to heat an...Ch. 6.11 - Prob. 132RPCh. 6.11 - Consider a Carnot heat-engine cycle executed in a...Ch. 6.11 - Prob. 134RPCh. 6.11 - Consider a Carnot refrigeration cycle executed in...Ch. 6.11 - Prob. 137RPCh. 6.11 - Consider two Carnot heat engines operating in...Ch. 6.11 - A heat engine operates between two reservoirs at...Ch. 6.11 - An old gas turbine has an efficiency of 21 percent...Ch. 6.11 - Prob. 141RPCh. 6.11 - Prob. 142RPCh. 6.11 - Prob. 143RPCh. 6.11 - The drinking water needs of a production facility...Ch. 6.11 - Prob. 145RPCh. 6.11 - Prob. 147RPCh. 6.11 - Prob. 148RPCh. 6.11 - Prob. 149RPCh. 6.11 - Prob. 150RPCh. 6.11 - Prob. 151RPCh. 6.11 - A heat pump with refrigerant-134a as the working...Ch. 6.11 - 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