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 |

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%.