Thermodynamics and Heat Engines

The annexed figure 1 shows one of the thermometers employed for this purpose, mounted on the piston of a steam-engine for observing the adiabatic relation between P and T for dry steam. The sensitive portion of the thermometer consisted of a differ ential loop L of fine platinum wire a thousandth of an inch in diameter and 1 inch in length. The fine wire was connected to thick platinum leads, insulated by being fused through a glass tube MM held in a gland in the centre of the piston. The platinum leads in the glass tube were connected to insulated copper leads, which were carried out to the measuring apparatus through a hole 2 ft. long bored through the piston rod. Since the ends of the fine wire, where it is attached to the thick platinum leads, cannot follow the rapid variations of temperature of the steam, it is necessary with this type of thermometer to compensate these end-effects by connecting a short loop of the same fine wire to the ends of the compensating leads CC. The quantity measured being the difference of resistance of the long and short loops, all such end-effects are automatically eliminated. Readings of temperature were taken with the aid of a periodic contact (mounted on the revolving shaft) which could be ad justed, while the engine was running, in such a way as to close the circuit of the galvanometer at any desired point of the It was found possible to read the temperature to one or two tenths of I° C at the maximum and minimum points, with the engine running at zoo rev./min. and a range of temperature of about 300° C between maximum and minimum. Readings taken at intermediate points, where the temperature was changing at the rate of more than 500° C per second, showed very good agreement, but could not be utilised in the calculation because the simultaneous values of the pressure could not be located with sufficient accuracy on the steep part of the indicator curve, whereas the maxima and minima could be measured with the greatest precision. The ports of the cylinder used in these experi ments were caulked with lead to prevent leakage, and the cylinder was heated by steam in the jackets and steam-chest to minimize condensation. The flywheel was belted to an electric motor and driven at a steady speed by a large storage battery. The observa tions covered a range of temperature from Ioo° to 420° C, but could not be extended beyond 15o lb. pressure by this method, owing to deficient strength of the engine and driving gear. The results obtained with several different thermometers and indi cators, showed that the adiabatic index for steam must be very nearly constant over this range of pressure and temperature with a value given by n+ i =13/3 in (a)), or 7 =1.300 in the relation (9) between P and V. Recent observations on the total heat H up to 4,000 lb. pressure, have shown that the same rela tion holds for dry steam with remarkable accuracy in the critical region, in spite of enormous variations in the ratio of the specific heats. The importance of this result in practice lies in the fact that it gives a very simple expression (6) for E or H in terms of P and V, or for V in terms of H and P, in addition to giving the simplest possible expressions for the work done in adiabatic expansion, or for the discharge through a nozzle, the utility of which can hardly be exaggerated in practical thermodynamics. Similar relations, but with 'y =1.40 or n=2.5, have long been applied to the case of atmospheric air, which forms the chief constituent of the working fluid in the internal combustion engine. But in the case of air the application is much more simple and obvious, because air obeys the gas equation aPV =RT very closely, and its specific heats vary very little with pressure under ordinary conditions.

The Energy Equation in Steady Flow.—The flow of a fluid through a pipe or any closed apparatus, is said to be "steady" when the mass M per second passing any cross-section X is the same at every point, and remains constant during the flow. This implies that the fluid is supplied at a steady rate by some external agent (e.g., a pump or boiler) at a constant pressure and temperature, in which case the whole apparatus traversed by the fluid will soon settle down into a steady state in which the values of P, V, and T remain constant at each point, though they will not be the same at different points, if the section X varies from point to point, or if the fluid receives heat or does work at a steady rate during its passage. It follows from the law of conservation of mass that, when the mass-flow M is constant at every point, the velocity U of the fluid at any section X is given in terms of V by the relation where k is a constant depending on the units employed.

A second relation follows from the law of conservation of energy, since the energy existing in any section must remain constant when the conditions are steady. The total energy carried into any section by the fluid per unit mass in thermal units will consist of its intrinsic energy E', together with the equivalent aP'V' of the work done by the pump, and with the kinetic energy of flow, reduced to thermal units by the factor 1/.1g. Thus the total energy carried in by the fluid may be

represented briefly by H'-FK'. Similarly the total energy carried out of the same section by the fluid may be represented by H"+K". But with the energy carried out we must include the equivalent IV/J of any work done by the apparatus, and any heat Q lost by radiation or convection, both measured per unit mass of the fluid passing through. Collecting the terms, the general equation may be written The steam-turbine may be taken as a typical example. H' —H" represents the drop of total heat of the fluid, or more briefly the 'Heat-drop,' between the inflow and outflow of any section. In an efficient machine, this heat-drop is very nearly equivalent to the external work IV done by the steam on the revolving blades. The external heat-loss Q is a small percentage of the whole. The kinetic energy K" of the steam leaving the section usually ex ceeds K', that of the steam entering and K"—K' represents a similar percentage loss. The greater part of the loss in a turbine is that due to internal friction, by which part of the available kinetic energy is reconverted into heat. This part of the loss is included in the total heat H" carried out by the steam. If there were no friction or heat-loss, the drop of total heat, representing heat converted into kinetic energy or work, would be that obtain able in frictionless adiabatic expansion between the same limits of pressure, which may be found from the tables and compared with the actual performance to estimate the efficiency. The method of doing this will be explained later, when some of the simpler applications of equation (I2) have been illustrated.

The Throttling Method.

The function of a throttle, or re ducing-valve, is to regulate the flow, or change the state of the fluid, by lowering the pressure without altering the total heat. The throttle, having no moving parts, cannot do any external work, so that W=o in equation (1 2 ). In this case, most of the kinetic energy is reconverted into heat by friction, so that K" can be made nearly equal to K' under favourable conditions. The equation then reduces to the form The chief use of the equation in this form is to find the value of the total heat H' at a high pressure by throttling to a lower pressure, such as atmospheric, and observing the temperature T". The total heat H" at the lower temperature and pressure may be regarded as known by equation (3) in terms of the specific heat S. Thus the required value of H' at T' and P' is given by (13) if the heat-loss Q can be determined. The best way of doing this is to employ a differential calorimeter as shown in fig. 2. The high pressure steam enters the centre pocket at the back and circulates round the thermometer tube (A) for measuring the initial temperature. The initial pressure is measured at the same point through the connection (D) to the high pressure gauge. The main current then divides right and left through the throttle tubes (E) and (F) to the side pockets (B) and (C) where the temperature of the throttled steam is measured. These pockets are precisely similar, and are lagged and jacketed with throttled steam in order to reduce heat-loss, which would other wise be rather large at high temperatures. The throttle tubes are fitted with a progressive series of throttles and baffles, designed to give maximum friction and reduce the kinetic energy to a negligible quantity. Using single and double dashes to distinguish the two sides, the flows M' and M" on either side, as defined where represents the total heat in the centre pocket. Whence H„=2H'—H", both of which are known from the observed temperatures t' and t". Since S is nearly constant for steam at atmospheric pressure, it usually suffices to correct the observed temperature r for heat-loss by adding (t'—t") M"/ (M' —M"), as in the following example. Starting with steam at 3,805 lb. pressure and 426.6° C, the observed temperatures on either side after throttling to 16 lb. were t' =120.3° C and r= I 14.I° C, the ratio M"/(M'—M") being 0.97. The correction to t' for heat-loss is 0.97X 6.2° =6.0°, giving 126.3° C for the corrected temperature, at which H„ = 652.4 cal. C, as given in the tables at 16 lb. This method is one of the simplest for measuring H at high pressures and temperatures, but cannot be applied if H is less than 64o cal., because the throttled steam would be wet. Thus in measuring H at the critical point, C, and 3,222 lb., where its value is only 554.4 cal. it is necessary to use the jacketed condenser method as described in the article CALORIMETRY. This method is rather more difficult, but has the advantage of apply ing equally to the case of water.