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 4, Problem 36P
To determine

The values of the final temperature and enthalpy.

Expert Solution & Answer
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Explanation of Solution

Given:

The mass of the refrigerant (m) is 0.13lbm.

The temperature of the mixture (T) is 30°F.

The quality of the mixture (x) is 80 percent or 0.8.

The spring force (F) is 37 lbf/in.

The diameter of the piston (D) is 12in.

Calculation:

Refer the table A-11E, “Saturated refrigerant-134a–Temperature table”, obtain the properties of refrigerant-134a at temperature of 30°F.

Specific volume of saturated liquid, vf= 0.01143ft3/lbm.

Specific volume of saturated vapor, vg= 4.4286ft3/lbm.

Saturation pressure, P1=Psat=9.868psia.

Write the initial specific volume of the piston-cylinder device (v1).

  v1=vf+x(vgvf)

  v1=0.01143ft3/lbm+(0.80)(4.4286ft3/lbm0.01143ft3/lbm)=3.5452ft3/lbm

Calculate the initial volume of the piston-cylinder device (V1).

  V1=mv1

  V1=(0.13lbm)(3.5452ft3/lbm)=0.4609ft3

Write the final volume (V2) for 50% increase in the volume.

  V2=1.5V1

  V2=1.5(0.4609ft3)=0.6913ft3

Write the area of the piston (Ap).

  Ap=πD24

Here, diameter of the piston is D.

Substitute 12in. for D in Equation (IV).

  Ap=π(12in.)24=π(12in.×1ft12in.)24=0.7854ft2

Write the distance that the piston (Δx) slides between the initial and final circumstances.

  Δx=ΔVAp=V2V1Ap

  Δx=0.6913ft30.4609ft30.7854ft2=0.2304ft30.7854ft2=0.2934ft

Here, change in volume is ΔV.

Write the difference in pressure (ΔP).

  ΔP=ΔFAp=kΔxAp

  ΔP=(37lbf/in.)(0.2934ft)(0.7854ft2)=(37lbf/in.)(0.2934ft×12in.1ft)(0.7854ft2×(12in.12ft)2)=1.152lbf/in.2=1.152psia

Here, change in force is ΔF, and spring constant is k.

Write the final pressure of the piston-cylinder device (P2).

  P2=P1+ΔP

  P2=9.868psia+1.152psia=11.02psia

Write the final specific volume of the piston-cylinder device (v2).

  v2=V2m

  v2=0.6913ft30.13lbm=5.318ft3/lbm

Refer the table A-13E, “Superheated refrigerant-134a table”, obtain the value of the final temperature and final enthalpy at final pressure of 11.02psia and final specific volume of 5.318ft3/lbm as 105°F and 125Btu/lbm.

Thus, the values of the final temperature and enthalpy are 105°F and 125Btu/lbm respectively.

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Chapter 4 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Does hfg change with pressure? How? Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Which process requires more energy: completely...Ch. 4 - In the absence of compressed liquid tables, how is...Ch. 4 - In 1775, Dr. William Cullen made ice in Scotland...Ch. 4 - Complete this table for H2O: Ch. 4 - Prob. 21PCh. 4 - Complete this table for H2O: Ch. 4 - Prob. 24PCh. 4 - Prob. 26PCh. 4 - Complete this table for refrigerant-134a: Ch. 4 - A 1.8-m3 rigid tank contains steam at 220°C....Ch. 4 - Prob. 29PCh. 4 - R-134a, whose specific volume is 0.6243 ft3/lbm,...Ch. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Refrigerant-134a at 200 kPa and 25°C flows through...Ch. 4 - The average atmospheric pressure in Denver...Ch. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - One pound-mass of water fills a 2.4264-ft3...Ch. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Water initially at 200 kPa and 300°C is contained...Ch. 4 - Saturated steam coming off the turbine of a steam...Ch. 4 - Water in a 5-cm-deep pan is observed to boil at...Ch. 4 - A cooking pan whose inner diameter is 20 cm is...Ch. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - A piston–cylinder device contains 0.005 m3 of...Ch. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - A rigid vessel contains 8 kg of refrigerant-134a...Ch. 4 - Prob. 63PCh. 4 - A piston–cylinder device initially contains 50 L...Ch. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - The air in an automobile tire with a volume of...Ch. 4 - The air in an automobile tire with a volume of...Ch. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - What is the principle of corresponding states? Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - Prob. 84PCh. 4 - Prob. 85PCh. 4 - Prob. 86PCh. 4 - Prob. 87PCh. 4 - What is the percentage of error involved in...Ch. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Prob. 93RQCh. 4 - Prob. 94RQCh. 4 - A tank contains argon at 600°C and 200 kPa gage....Ch. 4 - Prob. 96RQCh. 4 - Prob. 97RQCh. 4 - Prob. 98RQCh. 4 - Prob. 99RQCh. 4 - Prob. 100RQCh. 4 - Prob. 101RQCh. 4 - Prob. 102RQCh. 4 - A 4-L rigid tank contains 2 kg of saturated...Ch. 4 - The gage pressure of an automobile tire is...Ch. 4 - Prob. 105RQCh. 4 - Prob. 106RQCh. 4 - Prob. 107RQCh. 4 - Prob. 108RQCh. 4 - Prob. 109RQCh. 4 - Prob. 110RQCh. 4 - Prob. 111RQCh. 4 - Prob. 112RQ
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