A mass of air (molecular mass equal to 28.97 g/mol) at 150 kPa and 27 ‰is contained in a frictionless piston-cylinder device. At the initial state, the piston is resting on a pair of stops and the total volume of occupied by the air is 400 L. The mass of the piston is such that a 350 kPa pressure is needed to move it. The air is now heated until its volume has doubled. Draw the process on the PV diagram. Determine: (a) the final temperature; (b) the work done by the air; and (c) the total heat added into the gas. (Hint: you might want to use Table I

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A mass of air (molecular mass equal to
28.97 g/mol) at 150 kPa and 27 ‰is contained in a
frictionless piston-cylinder device. At the initial state,
the piston is resting on a pair of stops and the total
volume of occupied by the air is 400 L. The mass of
the piston is such that a 350 kPa pressure is needed
to move it. The air is now heated until its volume
has doubled. Draw the process on the PV diagram.
Determine: (a) the final temperature; (b) the work
done by the air; and (c) the total heat added into the
gas. (Hint: you might want to use Table I).

Table I
TABLE A-17
Ideal-gas properties of air
P.
kJ/kg
kJ/kg
kJ/(kg - K)
kJ/kg
kajkg
kJkg - K)
K
K
200
199.97
0.3363
142.56
1707.0
1.295 59
580
586.04
14.38
419.55
115.7
2.373 48
596.52
15.31
2.391 40
2.409.02
210
209.97
0.3087
149.69
1512.0
1.344 44
590
427.15 110.6
220
219.97
0.4890
156.82
1346.0
1.391 05
600
607.02
16.28
434.78
105.8
230
230.02
0.5477
164.00
1205.0
1.43557
610
617.53
17.30
442.42
101.2
2.426 44
240
240.02
0.6355
171.13
1084.0
1.478 24
620
628.07
18.36
450.09
96.92
2.443 56
178.28
638.63
19.84
457.78
92.84
2.460 48
2.477 16
250
250.05
0.7329
979.0
1.519 17
630
260
260.09
0.8405
185.45
887.8
1.558 48
640
649.22
20.64
465.50
88.99
270
270.11
0.9590
192.60
806.0
1.596 34
650
669.84
21.66
473.25
86.34
2.493 64
280.13
1.0889
199.75
1.632 79
670.47
23.13
481.01
2509 85
738.0
706.1
260
660
285
285.14
1.1584
203.33
1.650 55
670
681.14
24.46
488.81
78.61
2525 89
25. 85
27.29
28.80
290
290.16
1.2311
206.91
676.1
1.868 02
680
691.82
496.62
75.50
2541 75
72.56
1.3068
1.3860
235
295.17
210.49
647.9
1.685 15
690
702.52
504.45
2.557 31
300
300.19
214.07
621.2
1.702 03
700
713.27
512.33
69.76
257277
520.23
1.4686
1.5546
305.22
217.67
596.0
1.718 65
710
724.04
67.07
2.568 10
30.38
32.02
305
310
310.24
221.25
572.3
1.734 98
720
734.82
528.14
64.53
2603 19
2618 03
2.632 80
1,6442
224.85
536.07
62.13
549.8
528.6
315
315.27
1.751 06
730
745.62
33.72
320
320 29
1.7375
228.42
1.766 90
740
756.44
35.50
544.02
50.82
325
325.31
1.8345
232.02
508.4
1.782 49
750
767.29
37.35
551.99
57.63
2.647 S7
330
330.34
1.9352
235.61
489.4
1.797 83
760
778.18
39.27
560.01
55.54
2.661 76
340
340.42
2.149
242.82
454.1
1.827 90
780
800.03
43.35
576.12
51.64
2 690 13
350.49
422.2
821.95
2.71787
2.379
2.626
350
250.02
1.857 08
800
47.75
582.30
48.08
1.885 43
1.918 13
1.94001
360
360.58
257.24
393.4
820
843.98
52.59
608.59
44.84
2.745 04
370
370.67
2.892
264.46
367.2
840
B66.08
57.60
624.95
41.85
2.771 70
380
380.77
3.176
271.69
343.4
850
688.27
63.09
641.40
39.12
2.797 83
390
390.88
3.481
278.93
321.5
1.966 33
680
910.56
68.98
657.95
36.61
2.823 44
€74.58
2848 56
3.806
4.153
286.16
293.43
400
400.98
301.6
1.991 94
900
932.93
75.29
34.31
283.3
2.016 99
20
955.38
82.05
691.28
708.06
2.873 24
410
411.12
32.18
4.522
300.69
266.6
89.28
2.041 42
2.065 33
2.068 70
420
421.26
977.92
30.22
2.887 45
2.921 28
307.99
315.30
430
431.43
4.915
251.1
960
1000.55
97.00
725.02
28.40
440
441.61
5.332
236.8
980
1023.25
105.2
741.98
26.73
2944 68
5.775
322.62
223.6
2.11161
2.134 07
2.156 04
450
451.80
1000
1046.04
114.0
758.94
25.17
2.967 70
2.990 34
329.97
337.32
462.02
211.4
1068.89
776.10
1020
1040
6.245
123.4
23.72
470
472.24
6.742
200.1
1091.85
133.3
793.36
22.39
3.01260
3.034 49
3.056 08
480
482.49
7.268
344.70
189.5
2.177 60
1060
1114.86
143.9
810.62
21.14
490
492.74
7.824
352.06
179.7
2.198 76
1080
1137.89
156.2
827 88
19.98
500
503.02
a.411
359.49
170.6
2.219 52
1100
1161.07
167.1
845.33
18.896
3.077 32
510
513.32
9.031
366.92
162.1
2.239 93
1120
1184.26
179.7
862.79
17.886
3.098 25
520
530
523.63
9.684
374.36
154.1
2.259 97
1140
1207.57
193.1
Be0.35
16.946
3.11883
533.98
10.37
146.7
2.279 67
1230.92
207.2
89791
16.084
3.139 16
381.84
389.34
1160
540
544.35
11.10
139.7
2.299 06
1180
1254.34
2222
915.57
15.241
3.159 16
550
554.74
11.86
396.86
133.1
2.318 09
1200
1277.79
238.0
93333
14.470
3.178 68
560
565.17
12.66
404.42
127.0
2.336 85
1220
1301.31
254.7
951.09
13.747
3.196 34
570
575.59
13.50
411.97
121.2
2.355 31
1240
1324.93
272.3
968.95
13.069
3.21751
898
Transcribed Image Text:Table I TABLE A-17 Ideal-gas properties of air P. kJ/kg kJ/kg kJ/(kg - K) kJ/kg kajkg kJkg - K) K K 200 199.97 0.3363 142.56 1707.0 1.295 59 580 586.04 14.38 419.55 115.7 2.373 48 596.52 15.31 2.391 40 2.409.02 210 209.97 0.3087 149.69 1512.0 1.344 44 590 427.15 110.6 220 219.97 0.4890 156.82 1346.0 1.391 05 600 607.02 16.28 434.78 105.8 230 230.02 0.5477 164.00 1205.0 1.43557 610 617.53 17.30 442.42 101.2 2.426 44 240 240.02 0.6355 171.13 1084.0 1.478 24 620 628.07 18.36 450.09 96.92 2.443 56 178.28 638.63 19.84 457.78 92.84 2.460 48 2.477 16 250 250.05 0.7329 979.0 1.519 17 630 260 260.09 0.8405 185.45 887.8 1.558 48 640 649.22 20.64 465.50 88.99 270 270.11 0.9590 192.60 806.0 1.596 34 650 669.84 21.66 473.25 86.34 2.493 64 280.13 1.0889 199.75 1.632 79 670.47 23.13 481.01 2509 85 738.0 706.1 260 660 285 285.14 1.1584 203.33 1.650 55 670 681.14 24.46 488.81 78.61 2525 89 25. 85 27.29 28.80 290 290.16 1.2311 206.91 676.1 1.868 02 680 691.82 496.62 75.50 2541 75 72.56 1.3068 1.3860 235 295.17 210.49 647.9 1.685 15 690 702.52 504.45 2.557 31 300 300.19 214.07 621.2 1.702 03 700 713.27 512.33 69.76 257277 520.23 1.4686 1.5546 305.22 217.67 596.0 1.718 65 710 724.04 67.07 2.568 10 30.38 32.02 305 310 310.24 221.25 572.3 1.734 98 720 734.82 528.14 64.53 2603 19 2618 03 2.632 80 1,6442 224.85 536.07 62.13 549.8 528.6 315 315.27 1.751 06 730 745.62 33.72 320 320 29 1.7375 228.42 1.766 90 740 756.44 35.50 544.02 50.82 325 325.31 1.8345 232.02 508.4 1.782 49 750 767.29 37.35 551.99 57.63 2.647 S7 330 330.34 1.9352 235.61 489.4 1.797 83 760 778.18 39.27 560.01 55.54 2.661 76 340 340.42 2.149 242.82 454.1 1.827 90 780 800.03 43.35 576.12 51.64 2 690 13 350.49 422.2 821.95 2.71787 2.379 2.626 350 250.02 1.857 08 800 47.75 582.30 48.08 1.885 43 1.918 13 1.94001 360 360.58 257.24 393.4 820 843.98 52.59 608.59 44.84 2.745 04 370 370.67 2.892 264.46 367.2 840 B66.08 57.60 624.95 41.85 2.771 70 380 380.77 3.176 271.69 343.4 850 688.27 63.09 641.40 39.12 2.797 83 390 390.88 3.481 278.93 321.5 1.966 33 680 910.56 68.98 657.95 36.61 2.823 44 €74.58 2848 56 3.806 4.153 286.16 293.43 400 400.98 301.6 1.991 94 900 932.93 75.29 34.31 283.3 2.016 99 20 955.38 82.05 691.28 708.06 2.873 24 410 411.12 32.18 4.522 300.69 266.6 89.28 2.041 42 2.065 33 2.068 70 420 421.26 977.92 30.22 2.887 45 2.921 28 307.99 315.30 430 431.43 4.915 251.1 960 1000.55 97.00 725.02 28.40 440 441.61 5.332 236.8 980 1023.25 105.2 741.98 26.73 2944 68 5.775 322.62 223.6 2.11161 2.134 07 2.156 04 450 451.80 1000 1046.04 114.0 758.94 25.17 2.967 70 2.990 34 329.97 337.32 462.02 211.4 1068.89 776.10 1020 1040 6.245 123.4 23.72 470 472.24 6.742 200.1 1091.85 133.3 793.36 22.39 3.01260 3.034 49 3.056 08 480 482.49 7.268 344.70 189.5 2.177 60 1060 1114.86 143.9 810.62 21.14 490 492.74 7.824 352.06 179.7 2.198 76 1080 1137.89 156.2 827 88 19.98 500 503.02 a.411 359.49 170.6 2.219 52 1100 1161.07 167.1 845.33 18.896 3.077 32 510 513.32 9.031 366.92 162.1 2.239 93 1120 1184.26 179.7 862.79 17.886 3.098 25 520 530 523.63 9.684 374.36 154.1 2.259 97 1140 1207.57 193.1 Be0.35 16.946 3.11883 533.98 10.37 146.7 2.279 67 1230.92 207.2 89791 16.084 3.139 16 381.84 389.34 1160 540 544.35 11.10 139.7 2.299 06 1180 1254.34 2222 915.57 15.241 3.159 16 550 554.74 11.86 396.86 133.1 2.318 09 1200 1277.79 238.0 93333 14.470 3.178 68 560 565.17 12.66 404.42 127.0 2.336 85 1220 1301.31 254.7 951.09 13.747 3.196 34 570 575.59 13.50 411.97 121.2 2.355 31 1240 1324.93 272.3 968.95 13.069 3.21751 898
Table I
TABLE A-17
(Continued)
P,
kJ/kg
kJ/(ke - K)
P.
kJ/kg
K
kJ/kg
K
kJ/kg
kJkg - K)
1260
1348.55
290.8
986.90
12.435
3.236 38
1600
1757.57
791.2
1298.30
5.804
3.52364
1280
1372.24
310.4
1004.76
11.835
3.255 10
1620
1782.00
834.1
1316.96
5.574
3.538 79
1300
1395.97
330.9
1022.82
11.275
3.273 45
1640
1806.46
878.9
1335.72
5.355
3.55381
10.747
10.247
1320
1419.76
352.5
1040.88
3.291 60
1860
1830.96
925.6
1354,48
5.147
3.568 67
1340
1443.60
375.3
1058.94
3.309 59
1680
1855.50
974.2
1373.24
4.949
3.583 35
1360
1467.49
399.1
1077.10
9.780
3.327 24
1700
1880.1
1025
1392.7
4.761
3.5979
1380
1491.44
424.2
1095.26
9.337
3.344 74
1750
1941.6
1161
1439.8
4.326
3.6336
1400
1515.42
450.5
1113.52
8.919
3.362 00
1800
2003.3
1310
1487.2
3.944
3.6684
3.601
3.295
1420
1539.44
478.0
1131.77
8.526
3.37901
1850
2065.3
1475
1534.9
3.7023
1440
1563.51
506.9
1150.13
8.153
3.395 86
1900
2127.4
1655
1582.6
3.7354
1460
1587.63
537.1
1168.49
7.801
3.41247
1950
2189.7
1852
1630.6
3.022
3.7677
1480
1611.79
568.8
1186.95
7.468
3.428 92
2000
2252.1
2068
1678.7
2.776
3.7994
2303
2559
2837
2.555
1205.41
1223.87
1500
1635.97
601.9
7.152
3.445 16
2050
2314.6
1726.8
3.8303
2377.4
3.8605
3.8901
1520
1660.23
636.5
6.854
3.461 20
2100
1775.3
2.356
1540
1684.51
672.8
1242.43
6.569
3.477 12
2150
2440.3
1823.8
2.175
2.012 3.9191
1560
1580
1708.82
710.5
1260.99
6.301
3.492 76
2200
2503.2
3138
1872.4
1733.17
750.0
1279.65
6.046
3.508 29
2250
2566.4
3464
1921.3
1.864 3.9474
Source: Konneth Wark, Thermodynamics, 4th ed., McGraw-till, New York, 1983, pp. 785-786, table A-SM. Originaty published in J. H.
Keenan and J. Kaye, Gas Tables, Wiley, New York, 1948.
899
Transcribed Image Text:Table I TABLE A-17 (Continued) P, kJ/kg kJ/(ke - K) P. kJ/kg K kJ/kg K kJ/kg kJkg - K) 1260 1348.55 290.8 986.90 12.435 3.236 38 1600 1757.57 791.2 1298.30 5.804 3.52364 1280 1372.24 310.4 1004.76 11.835 3.255 10 1620 1782.00 834.1 1316.96 5.574 3.538 79 1300 1395.97 330.9 1022.82 11.275 3.273 45 1640 1806.46 878.9 1335.72 5.355 3.55381 10.747 10.247 1320 1419.76 352.5 1040.88 3.291 60 1860 1830.96 925.6 1354,48 5.147 3.568 67 1340 1443.60 375.3 1058.94 3.309 59 1680 1855.50 974.2 1373.24 4.949 3.583 35 1360 1467.49 399.1 1077.10 9.780 3.327 24 1700 1880.1 1025 1392.7 4.761 3.5979 1380 1491.44 424.2 1095.26 9.337 3.344 74 1750 1941.6 1161 1439.8 4.326 3.6336 1400 1515.42 450.5 1113.52 8.919 3.362 00 1800 2003.3 1310 1487.2 3.944 3.6684 3.601 3.295 1420 1539.44 478.0 1131.77 8.526 3.37901 1850 2065.3 1475 1534.9 3.7023 1440 1563.51 506.9 1150.13 8.153 3.395 86 1900 2127.4 1655 1582.6 3.7354 1460 1587.63 537.1 1168.49 7.801 3.41247 1950 2189.7 1852 1630.6 3.022 3.7677 1480 1611.79 568.8 1186.95 7.468 3.428 92 2000 2252.1 2068 1678.7 2.776 3.7994 2303 2559 2837 2.555 1205.41 1223.87 1500 1635.97 601.9 7.152 3.445 16 2050 2314.6 1726.8 3.8303 2377.4 3.8605 3.8901 1520 1660.23 636.5 6.854 3.461 20 2100 1775.3 2.356 1540 1684.51 672.8 1242.43 6.569 3.477 12 2150 2440.3 1823.8 2.175 2.012 3.9191 1560 1580 1708.82 710.5 1260.99 6.301 3.492 76 2200 2503.2 3138 1872.4 1733.17 750.0 1279.65 6.046 3.508 29 2250 2566.4 3464 1921.3 1.864 3.9474 Source: Konneth Wark, Thermodynamics, 4th ed., McGraw-till, New York, 1983, pp. 785-786, table A-SM. Originaty published in J. H. Keenan and J. Kaye, Gas Tables, Wiley, New York, 1948. 899
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