Use the ideal-gas air Table A.7 to evaluate the heat

Fundamentals of Thermodynamcs | 8th Edition | ISBN: 9781118131992 | Authors: Claus Borgnakke, Richard E. Sonntag

Problem 128HP Chapter 3

Fundamentals of Thermodynamcs | 8th Edition

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Fundamentals of Thermodynamcs | 8th Edition | ISBN: 9781118131992 | Authors: Claus Borgnakke, Richard E. Sonntag

Fundamentals of Thermodynamcs | 8th Edition

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Problem 128HP

Use the ideal-gas air Table A.7 to evaluate the heat capacity Cp at 300 K as a slope of the curve h(T) by Δh/ΔT. How much larger is it at 1000 K and at 1500 K?

TABLE A.7.1 Ideal Gas Properties of Air, Standard Entropy at 0.1-MPa (1-Bar) Pressure

T

u

h

ST0

T

u

h

ST0

(K)

(kJ/kg)

(kJ/kg)

(kJ/kg-K)

(K)

(kJ/kg)

(kJ/kg)

(kJ/kg-K)

200

142.77

200.17

6.46260

1100

845.45

1161.18

8.24449

220

157.07

220.22

6.55812

1150

889.21

1219.30

8.29616

240

171.38

240.27

6.64535

1200

933.37

1277.81

8.34596

260

185.70

260.32

6.72562

1250

977.89

1336.68

8.39402

280

200.02

280.39

6.79998

1300

1022.75

1395.89

8.44046

290

207.19

290.43

6.83521

1350

1067.94

1455.43

8.48539

298.15

213.04

298.62

6.86305

1400

1113.43

1515.27

8.52891

300

214.36

300.47

6.86926

1450

1159.20

1575.40

8.57111

320

228.73

320.58

6.93413

1500

1205.25

1635.80

Step-by-Step Solution:

Solution 128HP

Step 1 of 3:

We are going to find the heat capacity Cp of the ideal gas for the given temperature and to compare the increase with respect to temperatures 1000K and 1500K.

The first temperature T = 300 K

The temperature values are taken from the table A.7 near the temperature T.

T1 = 320 K

T2 = 290 K

The specific enthalpies are given for the temperatures T1 and T2

h1 = 290.43 kJ/kg

h2 = 320.58 kJ/kg

The specific heat can be calculated from the slope of the h-T curve at T.

Putting the values

The heat capacity of the ideal gas at 300 K is 1.0049 kJ/kg.K

Step 2 of 3:

To compare the heat capacity at 1000 K and 1500 K with the previous value:

The heat capacity at T = 1000 K

The temperature values are taken from the table A.7 near the temperature T.

T1 = 1050 K

T2 = 950 K

The specific enthalpies are given for the temperatures T1 and T2

h1 = 989.44 kJ/kg

h2 = 1103.48 kJ/kg

The specific heat can be calculated from the slope of the h-T curve at T.

Putting the values

The percentage increase in Cp 

 

 

The increase in the Cp is approximately 14%.

Step 3 of 3

Chapter 3, Problem 128HP is Solved
Textbook: Fundamentals of Thermodynamcs
Edition: 8th
Author: Claus Borgnakke, Richard E. Sonntag
ISBN: 9781118131992

This textbook survival guide was created for the textbook: Fundamentals of Thermodynamcs , edition: 8th. The answer to “Use the ideal-gas air Table A.7 to evaluate the heat capacity Cp at 300 K as a slope of the curve h(T) by ?h/?T. How much larger is it at 1000 K and at 1500 K?TABLE A.7.1 Ideal Gas Properties of Air, Standard Entropy at 0.1-MPa (1-Bar) PressureTuhST0TuhST0(K)(kJ/kg)(kJ/kg)(kJ/kg-K)(K)(kJ/kg)(kJ/kg)(kJ/kg-K)200142.77200.176.462601100845.451161.188.24449220157.07220.226.558121150889.211219.308.29616240171.38240.276.645351200933.371277.818.34596260185.70260.326.725621250977.891336.688.39402280200.02280.396.7999813001022.751395.898.44046290207.19290.436.8352113501067.941455.438.48539298.15213.04298.626.8630514001113.431515.278.52891300214.36300.476.8692614501159.201575.408.57111320228.73320.586.9341315001205.251635.808.61208340243.11340.706.9951515501251.551696.458.65185360257.53360.867.0527616001298.081757.338.69051380271.99381.067.1073516501344.831818.448.72811400286.49401.307.1592617001391.801879.768.76472420301.04421.597.2087517501438.971941.288.80039440315.64441.937.2560718001486.332002.998.83516460330.31462.347.3014218501533.872064.888.86908480345.04482.817.3449919001581.592126.958.90219500359.84503.367.3869219501629.472189.198.93452520374.73523.987.4273620001677.522251.588.96611540389.69544.697.4664220501725.712314.138.99699560404.74565.477.5042221001774.062376.829.02721580419.87586.357.5408421501822.542439.669.05678600435.10607.327.5763822001871.162502.639.08573620450.42628.387.6109022501919.912565.739.11409640465.83649.537.6444823001968.792628.969.14189660481.34670.787.6771723502017.792692.319.16913680496.94692.127.7090324002066.912755.789.19586700512.64713.567.7401024502116.142819.379.22208720528.44735.107.7704425002165.482883.069.24781740544.33756.737.8000825502214.932946.869.27308760560.32778.467.8290526002264.483010.769.29790780576.40800.287.8574026502314.133074.779.32228800592.58822.207.8851427002363.883138.879.34625850633.42877.407.9520727502413.733203.069.36980900674.82933.158.0158128002463.663267.359.39297950716.76989.448.0766728502513.693331.739.415761000759.191046.228.1349329002563.803396.199.438181050802.101103.488.1908129502613.993460.739.460251100845.451161.188.2444930002664.273525.369.48198TABLE A7.2 The Isentropic Relative Pressure and Relative Volume FunctionsT[K]PrvrT[K]PrvrT[K]Prvr2000.2703493.4770023.16020.15519001327.50.954452200.3770389.1572025.74218.65219501485.80.875212400.5109313.2774028.54217.28920001658.60.804102600.6757256.5876031.57316.05220501847.10.740122800.8756213.2678034.85114.92521002052.10.682422900.9899195.3680038.38813.89721502274.80.63027298.151.0907182.2985048.46811.69522002516.20.583053001.1146179.4990060.5209.916922502777.50.540203201.3972152.7395074.8158.467723003059.90.501243401.7281131.20100091.6517.276023503364.60.465763602.1123113.651050111.356.288524003693.00.433383802.554899.1881100134.255.464124504046.20.403784003.061287.1371150160.734.771425004425.80.376694203.637377.0031200191.174.185925504833.00.351854404.289268.4091250226.023.688026005269.50.329034605.023361.0661300265.723.262626505736.70.308054805.846654.7481350310.742.897127006236.20.288725006.766349.2781400361.622.581727506769.70.270895207.790044.5141450418.892.308328007338.70.254435408.925740.3441500483.162.070328507945.10.2392156010.18236.6761550554.961.862529008590.70.2251158011.56833.4361600634.971.680429509277.20.2120560013.09230.5611650723.861.520073000100070.1999262014.76628.0011700822.331.37858 64016.59825.7131750931.141.25330 66018.60023.66218001051.051.14204 68020.78421.81818501182.91.04294 70023.16020.15519001327.50.95445” is broken down into a number of easy to follow steps, and 61 words. Since the solution to 128HP from 3 chapter was answered, more than 321 students have viewed the full step-by-step answer. Fundamentals of Thermodynamcs was written by and is associated to the ISBN: 9781118131992. This full solution covers the following key subjects: Table, pressure, relative, air, ideal. This expansive textbook survival guide covers 7 chapters, and 1462 solutions. The full step-by-step solution to problem: 128HP from chapter: 3 was answered by , our top Engineering and Tech solution expert on 08/03/17, 05:05AM.

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