Page:Popular Science Monthly Volume 76.djvu/247

ing processes in its operation would be called a perfect engine. In such an engine the degeneration $H_{2}/T_{2}$ above mentioned would be equal to the regeneration $H_{1}/T_{1}$ so that for a perfect engine we should have

$H_{2}/T_{2}=H_{1}/T_{1}$	(12)
or
$T_{1}/T_{2}=H_{1}/H_{2}$	(13)

Substituting the value of $H_{2}$ from equation (9) in equation (12) or (13), and solving for $W$, we have

$W={\frac {T_{1}-T_{2}}{T}}_{1}H_{1}$}}

(14)

This equation shows that the efficiency of any perfect engine working between the temperatures $T_{1}$ and $T_{2}$ would be equal to $[(T_{1}-T_{2})/T_{1}]$.

Lord Kelvin's definition of the ratio of two temperatures may be understood with the help of equation (13) in which $H_{1}$ and $H_{2}$ are the amounts of heat taken in and given out by a perfect engine during a given time, and $T_{1}$ and $T_{2}$ are the temperatures between which the engine is working.

Efficiencies of Engines in Practise.—A fraction of the heat which is delivered to an engine with the steam which drives the engine is converted into work. In order that this fraction may be large, the ratio $T_{1}/T_{2}$ must be as large as possible, and sweeping processes must be obviated as much as possible in the operation of the engine; $T_{1}$ being the temperature of the steam supplied to the engine, and $T_{2}$ being the temperature of the exhaust. The ratio of the initial temperature to the final temperature of the expansion steam or gas in an engine depends upon the ratio of the initial volume to the final volume of the steam or gas.

In order that moderately small cylinders^[1] may be used for the development of a given amount of power, the initial pressure of the steam or gas must be high; and in order that the final temperature may not be lower than atmospheric or available condenser water temperatures, the initial temperature must be high. The first point concerning high initial pressures is exemplified in the operation of the ordinary gas or gasoline engine in which the mixed charge of gas and air is highly compressed before it is exploded.

In the gas engine the initial temperature is the temperature of the

1. The objections to large cylinders are: (a) their great cost, (b) the great amount of heat radiated by them, (c) the great amount of cylinder condensation in a large cylinder as explained later, and (d) the great amount of piston friction and cost of lubrication.