Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

is subtracted from 9.403 cu. ft., since the volume is less for A pressure of 44.7 lb. than for a pressure of 44 lb.

9.268 X 14 129.752 cu. ft. EXAMPLE 5.–Find the weight of 40 cu. ft. of steam at a temperature of 2540 F.

SOLUTION.—The weight of 1 cu. ft. of steam at 254.0020, from the table, is .078839 lb. Neglecting the .0020, the weight of 40 cu. ft. is, therefore,

.078839 X 40 3.15356 lb. EXAMPLE 6.-How many pounds of steam at 64 lb. pressure, absolute, are required to raise the temperature of 300 lb. of water from 40° to 130° F., the water and steam being mixed ?

SOLUTION.—The number of heat units required to raise 1 lb. from 400 to 1300 is 130 — 40 90 B. T. U. (Actually a little more than 90 would be required, but the above is near enough for all practical purposes.) Then, to raise 300 lb. from 400 to 130° requires 90 X 300 = 27,000 B. T. U. This quantity of heat must necessarily come from the steam. Now, 1 lb. of steam at 64 lb. pressure gives up, in condensing, its latent heat of vaporization, or 905.9 B. T. U. But, in addition to its latent heat, each pound of steam on condensing must give up an additional amount of heat in fall to 130°. Since the original temperature of the steam was 296.805° F. (see table), each pound gives up by its fall of temperature 296.805 — 130 = 166.805 B.T. U. Therefore, each pound of the steam gives up a total of 905.9 + 166.805 1,072.705 B. T. U.

27,000 at will, therefore, take

= 25.17 lb. of steam to

1,072.705 accomplish the desired result.

With the steam tables a reliable thermometer may be used for ascertaining the pressure of saturated steam or for testing the accuracy of a steam gauge. The temperature of the steam being measured by the thermometer, the corresponding absolute pressure is found from the steam tables; the gauge pressure is then found by subtracting 14.7 from the absolute pressure. Thus, the temperature of the steam in a condenser being 142°, we find from the steam tables that the correspond. ing absolute pressure is 3 lb. per sq. in., nearlv.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

1 2 3 4 5

102.018 70.040 1,043.015 1,113.055 .003027 330.4 20,623 126.302 94.368 1,026.094 1,120.462.005818 171.9 10,730 141.654 109.764 1,015.380 1,125.144 .008522 117.3 7,325 153.122 | 121.271 1,007.370 1,128.641 .011172 89.51

5,588 162.370 130.563 1,000.899 1,131.462 .013781 | 72.56 4,530

[blocks in formation]

1,646

14.69 212.000 180.531

966.069 1,146.600 .037928 26.37

15
16
17
18
19

213.067 | 181.608
216.347 184.919
219.452 188.056
222.424 191.058
225.255 193.918

965.318 1,146.926.038688 25.85 1,614
963.007 1,147.926.041109 24.33 1,519
960.818 1,148.874 .043519 22.98 1,434
958.721 1,149.779 .045920 21.78 1,359
956.725 1,150.643 .048312 20.70 1,292

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small]

20 227.964 196.655 954.814 1,151.469.050696 | 19.730 22 233.069 201.817 | 951.209 | 1,153.026 .055446 18.040 24 237.803 206.610 947.861 | 1,154.471 .060171 16.620 26 242.225 211.089 944.730 1,155.819 .064870 15.420 28 246.376 215.293 941.791 1,157.084.069545 14.380

1,231.0 1,126.0 1,038.0

962.3 897.6

30 250.293 219.261 939.019 1,158.280 .074201 13.480 32 254.002 223.021 936.389 | 1,159.410 .078839 | 12.680 34 257.523 226.594 933.891 1,160.485 .083461 11.980 36 260.883 230.001 931.508 1,161.509 .088067 11.360 38 264.093 233.261 929.227 1,162.488.092657 10.790

841.3 791.8 948.0 708.8 673.7

40 267.168 236.386 927.040 1,163.426 .097231 10.280 42 270.122 239.389 924.940 1,164.329 .101794 9.826 44 272.965 242.275 922.919 1,165.194 .106345 9.403 46 275.704 245.061 920.968 1,166.029 .110884 9.018 48 278.348 247.752 919.084 1,166.836 .115411 8.665

642.0 613.3 587.0 563.0 540.9

50 280.904 250.355 917.260 1,167.615 .119927 52 283.381 252.875 915.494 | 1,168.369 .124433 54 285.781 255.321 913.781 1,169.102.128928 56 288.111 257.695 912.118 1,169.813.133414 58 290.374 260.002 910.501 1,170.503.137892

[blocks in formation]

60 292.575 262.248 908.928 1,171.176 .142362 62 294.717 264.433 907.396 -1,171.829 .146824 64 296.805 266.566 905.900 1,172.466 .151277 66 298.842 268.644 904.443 1,173.087 .155721 68 300.831 270.674 903.020 1,173.694 .160157

[blocks in formation]

70 302.774 272.657 901.629 1,174.286.164584 72 304.669 274.597 900.269 1,174.866.169003 74 306.526 276.493 898.938 1,175.431 .173417 76 308.344 278.350 897.635 1,175.985 .177825 78 310.123 280.170 896.359 1,176.529 .182229

[blocks in formation]

80 311.866 281.952 895.108 1,177.060 82 313.576 283.701 893.879 1,177.580 84 315.250 285.414 892.677 1,178.091 86 316.893 287.096 891.496 1,178.592 88 ! 318.510 | 288.750 890.335 | 1,179.085

.186627 .191017 .195401 .199781 .204155

5.358
5.235
5.118
5.006
4.898

334.5 326.8 319.5 312.5 305.8

[blocks in formation]

250 400.883 373.750 830.459 1,204.209 260 404.370 377.377 827.896 1,205.273 270 407.755 380.905 825.401 1,206.306 280 411.048 384.337 | 822.973 1,207.310 290 414.250 387.677 820.609 1,208.286 300 417.371 390.933 818.305 1,209.238

.547831 1.825
.568626 1.759
.589390 1.697
.610124 1.639
.630829 1.585
.651506 1.535

114.0 109.8 105.9 102.3 99.0 95.8

LOGARITHMS.

EXPONENTS. By the use of logarithms, the processes of multiplication, division, involution, and evolution are greatly shortened, and some operations may be performed that would be impossible without them. Ordinary logarithms cannot be applied to addition and subtraction.

The logarithm of a number is that exponent by which some fixed number, called the base, must be affected in order to equal the number. Any number may be taken as the base. Suppose we choose 4. Then the logarithm of 16 is 2, because 2 is the exponent by which 4 (the base) must be affected in order to equal 16, since 42 = 16. In this case, instead of reading 42 as 4 square, read it 4 exponent 2. With the same base, the logarithms of 64 and 8 would be 3 and 1.5, respectively, since 43 64, and 41.5 = 8. In these cases, as in the preceding, read 43 and 41.5 as 4 exponent 3, and 4 exponent 1.5, respectively.

Although any positive number except 1 can be used as a base and a table of logarithms calculated, but two numbers have ever been employed. For all arithmetical operations (except addition and subtraction) the logarithms used are called the Briggs, or common, logarithms, and the base used is 10. In abstract mathematical analysis, the logarithms used are variously called hyperbolic, Napierian, or natural logarithms, and the base is 2.718281828+. The common logarithm of any number may be converted into a Napierian logarithm by multiplying the common logarithm by 2.30258509+, which is usually expressed as 2.3026, and sometimes as 2.3. Only the common system of logarithms will be considered here.

Since in the common system the base is 10, it follows that, since 101 =

100, 103 = 1,000, etc., the logarithm (exponent) of 10 is 1, of 100 is 2, of 1,000 is 3, etc. For the sake of brevity in writing, the words “logarithm of” are abbreviated to "log.” Thus, instead of writing logarithm of 100 = 2, write log 100 = 2. When speaking, however, the words for which “ log" stands should always be pronounced in full.

10, 102

« ΠροηγούμενηΣυνέχεια »