THERMO-DYNAMICS.

It has been already stated that heat and power are mutually convertible, and that the power in the shape of heat which is necessary to raise a pound of water through one degree Fahrenheit, would, if utilised without waste in a thermo-dynamic engine, raise 772 lbs. through the height of 1 foot. A pound of water raised through a degree centigrade is equivalent to 1390 lbs. raised through the height of 1 foot. In every heat engine, the greater the extremes of temperature, or the hotter the boiler or source of heat and the colder the condenser or refrigerator, the larger will be the proportion of the heat utilised as power.

In a perfect steam engine, if a be the temperature of the boiler, reckoning from the point of absolute zero, and b be the temperature of the condenser, reckoning also from the point of absolute zero, the fraction of the entire heat cominunicated to the boiler which will be converted into mechanical effect, will Now it is clear if ab, or if the temperature of the

be

a

α

b

a-b boiler and condenser are the same, the value of becomes

α

equal to 0, or there is none of the heat utilised as power, whereas, on the other hand, if a be taken larger and larger, the value of the fraction becomes continually greater, indicating that by increasing the difference of the temperatures of the boiler and condenser, a great quantity of the heat expended is converted into mechanical effect, and by taking a= ∞, or infinity, the limit to which the fraction approaches is found to be unity, showing that in such a case, if it were possible of realisation, the whole of the heat would be converted into power.

The formula given by Professor Thomson for determining the power generated by a perfect thermo-dynamic engine, is as follows:

If S be the temperature of the source of heat, and T be the temperature of the refrigerator, both expressed in centigrade degrees; and if I denote the total heat in thermal units centigrade, entering the engine in a given time; and J be Joule's

POWER PRODUCIBLE IN A PERFECT ENGINE. 181

equivalent of 1390 lbs. raised one foot high by a centigrade degree;-then the power produced, or W the work performed, is

This formula may be expressed in words, as follows:

TO FIND THE POWER GENERATED BY A PERFECT ENGINE IMPELLED BY THE MOTIVE POWER OF HEAT.

RULE. From the temperature of the source or boiler, subtract the temperature of the condenser; divide the remainder by the sum of the temperature of the source and 274, and multiply the quotient by the total heat communicated to the engine per minute, expressed in the number of degrees through which it would raise one pound of water. Finally, multiply this product by 1390. The result is the number of pounds that the engine will raise a foot high in the minute. The temperatures are all taken in degrees centigrade.

Example. In a steam-engine working with a pressure of 14 atmospheres, the temperature of the steam in the boiler will be 215° centigrade, and the temperature of the condenser may be taken at 44.44° centigrade. If a grain of coal be burned per minute, the heat imparted every minute to a pound of water will be 905° centigrade. Now 215-44.44° = 170.56 and 215 + 274 = 489, and 170·56 divided by 489 = 0·35, which multiplied by 905 and by 1390 = 440 lbs. raised 1 foot high every minute, which as a grain of coal is burned every minute, is very nearly the same result as that before indicated.

Cheapest Source of Motive Power.-The cheapest source of a mechanical power that will be available in all situations, is, so far as we yet know, the combustion of coal. Electricity and galvanism have been proposed as motive powers, and may be used as such, but they are much more expensive than coal. Mr. Joule has ascertained by his experiments that a grain of zinc, consumed in a galvanic battery, will generate sufficient power to raise a weight of 145.6 lbs. through the height of one foot;

whereas a grain of coal, consumed by combustion, will generate sufficient power to raise 1261.45 lbs. to the height of 1 foot.

Moreover, it appears certain that Mr. Joule's estimate of the heating power of coal is too small. A pound of coal will, under favourable circumstances, evaporate 12 lbs. of water, which is equivalent to a pound of water being heated 2 degrees Fahrenheit by a grain of coal, or it is equivalent to 1544 lbs. raised through 1 foot. This is more than ten times the power genersted by a pound of zinc. But as thermo-electric engines, it is estimated, expend their energy about four times more beneficially than heat engines, the dynamic efficacy of a pound of zinc may be taken as about 4-10ths of that of a pound of coal. A ton of zinc, however, costs fifty or sixty times as much as a ton of coals, while it is not half so effective. There does not appear, therefore, to be the least chance of heat engines being superseded by electro-dynamic engines, of which zinc or some other metal supplies the motive force.

EXPANSION OF STEAM.

When air is compressed into a smaller volume, a certain amount of power is expended in accomplishing the compression, which power, as in the case of a bent spring, is given back again when the pressure is withdrawn. If, however, the air when compressed is suddenly dismissed into the atmosphere, the power expended in compression will be lost; and there is a loss of power, therefore, in dispensing with that power, which is recoverable by the expansion of the air to its original volume. Now the steam of an engine is in the condition of air already compressed; and unless the steam be worked in the cylinder expansively-which is done by stopping the supply from the boiler before the stroke is closed-there will be a loss of a certain proportion of the power which the steam would otherwise produce. If the flow of steam to an engine be stopped when the piston has performed one-half of the stroke, leaving the rest of the stroke to be completed by the expanding steam, then the efficacy of the steam will be increased 1.7 times beyond what it

1

MUDE OF COMPUTING BENEFIT OF EXPANSION. 183

would have been had the steam at half-stroke been dismissed without extracting more power from it; if the steam be stopped at one-third of the stroke, the efficacy will be increased 2·1 times; at one-fourth, 2.4 times; at one-fifth, 2.6 times; at onesixth, 2.8 times; at one-seventh, 3 times; and at one-eighth, 3.2 times.

TO FIND THE INCREASE OF EFFICIENCY ARISING FROM WORKING STEAM EXPANSIVELY.

RULE.-Divide the total length of the stroke by the distance (which call 1) through which the piston moves before the steam is cut off. The Neperian logarithm of the whole stroke expressed in terms of the part of the stroke performed with the full pressure of steam, represents the increase of efficiency due to expansion.

Example 1.—Suppose that the steam be cut off at ths of the stroke: what is the increase of efficiency due to expansion? Here it is plain that ths of the whole stroke is the same as of the whole stroke. The hyperbolic logarithm of 7.5 is 2.015, which increased by 1, the value of the portion performed with full pressure, gives 3.015 as the relative efficacy of the steam when expanded to this extent, instead of 1, which would have been the efficacy if there had been no expansion.

6

7 8

If the steam be cut of at 1, 2, 3, 4, 5, 8, or 3th of the stroke, the respective ratios of expansion will be 8, 4, 2·66, 2, 1·6, 1·33, and 114, of which the respective hyperbolic logarithms are 2.079, 1-386, 0.978, 0.693, 0-470, 0-285, and 0.131; and if the steam be cut off at 10, 10, 10, 10, fo, To, 10, 1‰, or ths of the stroke, the respective ratios of expansion will be 10, 5, 3·33, 2.5, 1·66, 1·42, 1.25, and 1·11, of which numbers the respective hyperbolic logarithms are 2.303, 1-609, 1-203, 0.916, 0.507, 0.351, 0.223, and 0.104. With these data it will be easy to compute the mean pressure of steam of any given initial pressure when cut off at any eighth part or any tenth part of the stroke, as we have only to divide the initial pressure of the steam in lbs. per square inch by the ratio of expansion, and to multiply the quo

tient by the hyperbolic logarithm, increased by 1, of the number representing the ratio, which gives the mean pressure through out the stroke in lbs. per square inch. Thus, if steam of 100 lbs. be cut off at half stroke, the ratio of expansion is 2, and 100 divided by 2 and multiplied by 1.693 84.65, which is the mean pressure throughout the stroke in lbs. per square inch. The terminal pressure is found by dividing the initial pressure by the ratio of expansion; thus, the terminal pressure of steam of 100 lbs. cut off at half stroke will be 100 divided by 2 = 50 lbs. per square inch,

Example 2.-What is the mean pressure throughout the stroke of steam of 200 lbs. per square inch cut off at th of the stroke?

=

Here 200 divided by 10 20, which, multiplied by 3.303 (the hyperbolic logarithm of 10 increased by 1) gives 66.04, which is the mean pressure exerted on the piston throughout the stroks in lbs. per square inch.

If the steam were cut off at 1th of the stroke instead of th, then we should have 200 divided by 8 = 25, which, multiplied by 3.079 (the hyperbolic logarithm of 8 increased by 1), gives 76.975 lbs., which would be the mean pressure on the piston throughout the stroke in such a case.

If the initial pressure of the steam were 3 lbs. per square inch, and the expansion took place throughout ths of the stroke, or the steam were cut off at th, then 3÷8=375, which × by 3.079 1.154625 lbs. per square inch of mean pressure.

There are various expedients for stopping off the supply of steam to the engine at any desired point of the stroke, which are described in my 'Catechism of the Steam Engine,' and which, consequently, it would be superfluous to recapitulate here. One mode is by the use of an expansion valve, and another mode is by extending the length of the face of the ordinary slide valve by which the steam is let into and out of the cylinder, which extension of the face is called lap or cover. For the purposes of this work it will be sufficient to recapitu late the mean pressure of the steam on the piston of an engine throughout the whole stroke, supposing the steam to be cut off