Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 7, Problem 121RQ
To determine

The ratio of maximum pressure to minimum pressure.

Expert Solution & Answer
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Explanation of Solution

Given:

The absolute temperature reservoir (TH) is 1.2TL.

The rate of heat rejected by heat pump (W˙net,in) is 5kW.

The mass flow rate (m˙) is 0.22kg/s.

Calculation:

Write the coefficient of performance of reversible heat pump (COPHP,rev).

  COPHP,rev=11TLTH

  COPHP,rev=1111.2=6

Write the coefficient of performance of a Carnot heat pump.

  COPHP=Q˙HW˙net,in        (I)

Rewrite Equation (I) to calculate the heat gained by the pump.

  Q˙H=W˙net,in×COPHP

  Q˙H=5kW×6=30kW

Write the heat transfer from the Carnot heat pump cycle (qH).

  qH=Q˙Hm˙

  qH=30kW0.22kg/s=30kW×kJ/skW0.22kg/s=136.36 kJ/kg

Obtain the temperature and pressure using the above calculated enthalpy of vaporization.

Refer to Table A-12, “Saturated pressure table” enthalpy of vaporization is 136.36 kJ/kg obtain the following properties using interpolation method.

Show the temperature and constant pressure at temperature of 548 K as in Table (1).

Temperature, °C

Enthalpy kJ/kgPressure kPa
57.88141.961600
y2136.36z2
62.87135.141800

Write the formula of interpolation method of two variables.

  y2=(x2x1)(y3y1)(x3x1)+y1        (II)

Here, the variables denoted by x and y are enthalpy and entropy.

Substitute x1=141.96 kJ/kg, x2=136.36 kJ/kg, x3=135.14 kJ/kg, y1=57.88°C, and y3=62.87°C in Equation (II).

  y2=(136.36141.96)(62.8757.88)(135.14141.96)+57.88=5.6×4.996.82+57.88=62°C

Substitute x1=141.96 kJ/kg, x2=136.36 kJ/kg, x3=135.14 kJ/kg, y1=1600 kPa, and  y3=1600 kPa in Equation (II).

  y2=(136.36141.96)(18001600)(135.14141.96)+1600=5.6×2006.82+1600=1764kPa

Calculate the lower temperature of the reservoir.

  TL=TH1.2=62°C1.2=(62+273.2)K1.2=279.3333 K280K

      =(280273.2)°C=6.8°C

Refer table A-11, “Saturated refrigerant-134a temperature table”, obtain pressure value at the temperature of 6.8°C is Pmin=372.55 kPa (using interpolation method).

Calculate the ratio of maximum pressure to minimum pressure.

  PmaxPmin=1764 kPa372.55 kPa=4.735

Thus, the ratio of maximum pressure to minimum pressure is s.

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Chapter 7 Solutions

Fundamentals of Thermal-Fluid Sciences

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