Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 6, Problem 75P

(a)

To determine

The temperature of the air at the exit.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The inlet pressure of Refrigerant (P3) is 20 psia.

The inlet quality of Refrigerant (x3) is 30%.

The outlet pressure of Refrigerant (P3) is 20 psia.

The outlet quality of steam (x4) is 1 (saturated vapor).

The inlet pressure of air (P1) is 14.7 psia.

The inlet temperature of air (T1) is 90°F.

The volume flow rate of air (V˙1) is 200 ft3/min.

The mass flow rate of refrigerant (m˙R) is 4 lbm/min.

Calculation:

Draw the schematic diagram for the evaporator section.

Fundamentals Of Thermal-fluid Sciences In Si Units, Chapter 6, Problem 75P

Write the formula to calculate the specific enthalpy of steam (h) from tables.

  h=hf+x(hfg)        (I)

Here, specific enthalpy of saturated liquid is hf, specific enthalpy of saturated liquid-vapor mixture is hfg and dryness fraction of water is x.

Write the ideal gas equation for specific volume of air (v).

  v=RTP        (II)

Here, gas constant for air is R, temperature of air is T, and the pressure of air is P.

Calculate the volume flow rate (V˙1) of the air at the inlet.

  V˙1=m˙av1        (III)

Here, mass flow rate of air is m˙a and specific volume of air is v1.

Write the expression for the mass balance.

  minmout=Δm

  minmout=0(For steady state)        (IV)

Here, mass of the fluid entering into the system is min, mass of fluid leaving out of the system is mout and change in mass is Δm.

Write the energy rate balance equation for a control volume.

  E˙inE˙out=dE˙system/dt

  E˙inE˙out=0(For steady state)        (V)

Here, total energy rate at inlet is E˙in, total energy rate at outlet is E˙out and change in net energy rate is dE˙system/dt.

Refer Table A-1E, “Gas constant of common gases”, obtain the gas constant of air as 0.3704psiaft3/lbmR.

Refer Table A-2E, “Ideal – gas specific heats of common gases”, obtain the constant pressure specific heat of air as 0.240Btu/lbm.°F.

Refer Table A-12E, “Saturated R-134a-Pressure table”, obtain the properties of saturated R-134a at pressure (P3) of 20 psia.

  hf=11.436Btu/lbmhfg=91.302 Btu/lbm

Substitute hf=11.436Btu/lbm, x3=0.3, and hfg=91.302Btu/lbm in Equation (I).

  h3=11.436Btu/lbm+(0.3)91.302Btu/lbm=38.83Btu/lbm

Refer Table A-12E, “Saturated R-134a-Pressure table”, obtain the specific enthalpy (h4) of saturated vapor of R-134aat pressure (P4) of 20 psia as 102.74Btu/lbm.

Substitute R=0.3704psiaft3/lbmR, T1=90°F, and P1=14.7psia in Equation (II).

  v1=RT1P1=0.3704psiaft3/lbmR(90°F)14.7psia=0.3704psiaft3/lbmR(90+460)R14.7psia

  v1=13.86ft3/lbm

Substitute V˙1=200ft3/min and v1=13.86ft3/lbm in Equation (III).

  m˙a=200ft3/min13.86ft3/lbm=14.43lbm/min

Rewrite Equation (I) for the mass flow rate of air (m˙a).

  m˙1=m˙2=m˙a

Here, mass flow rate of air at inlet is m˙1 and mass flow rate of air at outlet is m˙2.

Rewrite the Equation (I) for the mass flow rate of R-134a (m˙R).

  m˙3=m˙4=m˙R

Here, mass flow rate of R-134a at inlet is m˙3, and mass flow rate of R-134a at outlet is m˙4.

Rewrite Equation (II) for the energy balance in the steam heating system.

  m˙1h1+m˙3h3=m˙2h2+m˙4h4        (V)

Substitute m˙a=m˙1, m˙2=m˙a, m˙3=m˙R, and m˙R for m˙4 in Equation (V).

  m˙ah1+m˙Rh3=m˙ah2+m˙Rh4m˙R(h3h4)=m˙a(h2h1)m˙R(h3h4)=m˙acp(T2T1)

  T2=T1+m˙R(h3h4)m˙acp

Substitute h3=38.83 Btu/lbm, h4=102.74 Btu/lbm, cp=0.240 Btu/lbm.°F, m˙R=4 lbm/min, m˙a= , and T1=90°F in above  Equation.

  T2=90°F+4 lbm/min×(38.83 Btu/lbm102.74 Btu/lbm)14.43 lbm/min×0.240 Btu/lbm.°F=16.2°F

Thus, the temperature of the air at the exit is 16.2°F.

(b)

To determine

The rate of heat transfer from the air to the refrigerant.

(b)

Expert Solution
Check Mark

Explanation of Solution

Write the formula to calculate the rate of heat transfer from the air to the refrigerant (Qair,out).

  Qair,out=m˙acp(T2T1)

Substitute m˙a=14.43lbm/min, cp=0.240Btu/lbm°F, T2=16.24°F and T1=90°F in above Equation.

  Qair,out=(14.43lbm/min)(0.240Btu/lbm°F)(16.24°F90°F)=255.6Btu/min

Thus, the rate of heat transfer from the air to the refrigerant is 255.6Btu/min.

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Chapter 6 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - A house is maintained at 1 atm and 24°C, and warm...Ch. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - The kinetic energy of a fluid increases as it is...Ch. 6 - Prob. 23PCh. 6 - Air enters a nozzle steadily at 50 psia, 140°F,...Ch. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Air at 600 kPa and 500 K enters an adiabatic...Ch. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Air at 13 psia and 65°F enters an adiabatic...Ch. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Steam at 4 MPa and 400°C enters a nozzle steadily...Ch. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Helium is to be compressed from 105 kPa and 295 K...Ch. 6 - Carbon dioxide enters an adiabatic compressor at...Ch. 6 - Air is compressed from 14.7 psia and 60°F to a...Ch. 6 - Prob. 47PCh. 6 - An adiabatic gas turbine expands air at 1300 kPa...Ch. 6 - Steam flows steadily into a turbine with a mass...Ch. 6 - Prob. 50PCh. 6 - Prob. 51PCh. 6 - Prob. 52PCh. 6 - Prob. 53PCh. 6 - Prob. 54PCh. 6 - Refrigerant-134a is throttled from the saturated...Ch. 6 - Prob. 56PCh. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Prob. 62PCh. 6 - Prob. 63PCh. 6 - Prob. 64PCh. 6 - Prob. 65PCh. 6 - Prob. 66PCh. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Prob. 69PCh. 6 - Prob. 70PCh. 6 - A thin-walled double-pipe counter-flow heat...Ch. 6 - Prob. 72PCh. 6 - Prob. 73PCh. 6 - Prob. 74PCh. 6 - Prob. 75PCh. 6 - Prob. 77PCh. 6 - Prob. 78PCh. 6 - Prob. 79PCh. 6 - Prob. 80PCh. 6 - Prob. 81PCh. 6 - Prob. 82PCh. 6 - Prob. 83PCh. 6 - Prob. 84PCh. 6 - Prob. 85PCh. 6 - The components of an electronic system dissipating...Ch. 6 - Prob. 87PCh. 6 - Prob. 88PCh. 6 - Prob. 89PCh. 6 - Prob. 90PCh. 6 - Prob. 91PCh. 6 - Prob. 92PCh. 6 - Prob. 93PCh. 6 - A house has an electric heating system that...Ch. 6 - Prob. 95PCh. 6 - Refrigerant-134a enters the condenser of a...Ch. 6 - Prob. 97PCh. 6 - Prob. 98PCh. 6 - Prob. 99PCh. 6 - Prob. 100PCh. 6 - Air enters the duct of an air-conditioning system...Ch. 6 - Prob. 102PCh. 6 - A rigid, insulated tank that is initially...Ch. 6 - Prob. 105PCh. 6 - Prob. 106PCh. 6 - Prob. 107PCh. 6 - Prob. 108PCh. 6 - Prob. 109PCh. 6 - An air-conditioning system is to be filled from a...Ch. 6 - Prob. 111PCh. 6 - A 0.06-m3 rigid tank initially contains...Ch. 6 - A 0.3-m3 rigid tank is filled with saturated...Ch. 6 - Prob. 114PCh. 6 - A 0.3-m3 rigid tank initially contains...Ch. 6 - Prob. 116PCh. 6 - Prob. 117PCh. 6 - An insulated 40-ft3 rigid tank contains air at 50...Ch. 6 - A vertical piston–cylinder device initially...Ch. 6 - A vertical piston–cylinder device initially...Ch. 6 - The air in a 6-m × 5-m × 4-m hospital room is to...Ch. 6 - Prob. 124RQCh. 6 - Prob. 125RQCh. 6 - Prob. 126RQCh. 6 - Prob. 127RQCh. 6 - Prob. 128RQCh. 6 - Prob. 129RQCh. 6 - Prob. 130RQCh. 6 - Prob. 131RQCh. 6 - Prob. 132RQCh. 6 - Steam enters a nozzle with a low velocity at 150°C...Ch. 6 - Prob. 134RQCh. 6 - Prob. 135RQCh. 6 - Prob. 136RQCh. 6 - In large steam power plants, the feedwater is...Ch. 6 - Prob. 138RQCh. 6 - Prob. 139RQCh. 6 - Prob. 140RQCh. 6 - Prob. 141RQCh. 6 - Prob. 142RQCh. 6 - Prob. 143RQCh. 6 - Prob. 144RQCh. 6 - Prob. 145RQCh. 6 - Prob. 146RQCh. 6 - Repeat Prob. 6–146 for a copper wire ( = 8950...Ch. 6 - Prob. 148RQCh. 6 - Prob. 149RQCh. 6 - Prob. 150RQCh. 6 - Prob. 151RQCh. 6 - Prob. 152RQCh. 6 - Prob. 153RQCh. 6 - An adiabatic air compressor is to be powered by a...Ch. 6 - Prob. 156RQCh. 6 - Prob. 157RQCh. 6 - Prob. 158RQCh. 6 - Prob. 159RQCh. 6 - Prob. 160RQCh. 6 - Prob. 161RQCh. 6 - Prob. 162RQCh. 6 - Prob. 163RQCh. 6 - Prob. 164RQCh. 6 - Prob. 166RQCh. 6 - Prob. 167RQCh. 6 - Prob. 168RQCh. 6 - Prob. 169RQ
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