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

## Problem 128HP Chapter 3

Fundamentals of Thermodynamcs | 8th Edition

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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

##### 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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