EBK THERMODYNAMICS: AN ENGINEERING APPR
EBK THERMODYNAMICS: AN ENGINEERING APPR
8th Edition
ISBN: 9780100257054
Author: CENGEL
Publisher: YUZU
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Chapter 6.11, Problem 148RP
To determine

The cost of energy “vented out” by the fans in 1 h.

Expert Solution & Answer
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Answer to Problem 148RP

The cost of energy “vented out” by the fans in 1 h is $0.106_.

Explanation of Solution

Determine the density of air at the indoor conditions.

ρo=PoRTo (I)

Here, the house maintain a pressure is Po, the universal gas constant is R, and the house maintain a temperature is T0.

Determine interior volume of the house per hour

ν˙air=w×l (II)

Here, the width of the house is w and the length of the house is l.

Determine the mass flow rate of air vented out.

m˙air=ρoν˙air (III)

Determine the rate of energy loss by the ventilating fans.

Q˙loss,fan=m˙aircp(TindoorToutdoor) (IV)

Here, the specific heat of air at room temperature is cP, the indoor air vented out at temperature is Tindoor, and the outdoor air temperature is Toutdoor.

Determine the amount of electric energy loss by “vented out”.

Electric energy loss=Q˙loss,fan×Δt/COP (V)

Here, the fan takes time is Δt and the coefficient of performance of fan is COP.

Determine the amount of cost of the heat “vented out” per hour.

Moneyloss=(electricenergyloss)×(Unitcostofenergy) (VI)

Conclusion:

From the Table A-1, “Molar mass, gas constant, and critical-point properties” to obtain the value of gas constant of air as 0.287kPam3/kgK.

From the Table A-2a, “Ideal-gas specific heats of various common gases” to obtain the value of specific heat of air at room temperature as 1.0kJ/kg°C.

Substitute 92 kPa for Po, 0.287kPam3/kgK for R, and 22°C for To in Equation (I).

ρo=92kPa(0.287kPam3/kgK)×(22°C)=92kPa(0.287kPam3/kgK)×(22°C+273)=92kPa84.665kPam3/kg=1.0866kg/m3

     1.087kg/m3

Substitute 200m2/h for w and 2.8m/h for l in Equation (II).

ν˙air=(200m2/h)×(2.8m/h)=560m3/h

Substitute 1.087kg/m3 for ρo and 560m3 for ν˙air in Equation (III).

m˙air=(1.087kg/m3)×(560m3/h)=608.72kg/h=608.72kg/h×(1kg/s3600kg/h)=0.169kg/s

Substitute 0.169kg/s for m˙air, 1.0kJ/kg°C for cp, 33°C for Tindoor and 22°C for Toutdoor in Equation (IV).

Q˙loss,fan=(0.169kg/s)×(1.0kJ/kg°C)×(33°C22°C)=(0.169kg/s)×(1.0kJ/kg°C)×(11°C)=1.859kJ/s=1.859kJ/s×(1kW1kJ/s)

          =1.859kW

Substitute 1.859kW for Q˙loss,fan, 1 h for Δt, and 2.1 for COP in Equation (V).

Electric energy loss=(1.859kW)×(1h)/(2.1)=(1.859kW)×(0.47619h)=0.885238kWh

Substitute 0.885238kWh for electric energy loss, $0.12/kWh for unit cost of energy in Equation (VI).

Moneyloss=(0.885238kWh)×($0.12/kWh)=(0.885238kWh)×($0.12/kWh)=$0.106

Thus, the cost of energy “vented out” by the fans in 1 h is $0.106_.

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Chapter 6 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

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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