In a Carnot cycle for example, a cylinder containing the working fluid is put in contact with the heat source when the temperature of the working fluid is the same temperature as the heat source snd allowed to absorb heat and expand.
However, the scientific principles is well known and thoroughly established that for a transfer of thermal energy there most be a temperature difference.
This is supposed to be a "quasi-static" process that takes an "infinite" amount of time. A quasi-static process is defined as: "an idealized or imagined process where the change in state is made infinitesimally slowly so that at each instant, the system can be assumed to be at a thermodynamic equilibrium with itself and with the environment"
But again, how can you have a transfer of heat when everything is in a state of thermal equilibrium?
How can any engine, for that matter run "infinitesimally slowly?
So, relatively recently, Carnot's cycle has been reworked and the words "same temperature" has been changed to a "temperature infinitesimally less than TH". (Wikipedia article on Carnot cycle).
Well if the first proposition was scientifically untenable, altering the original meaning and intent is just disingenuous IMO.
Recently however, I came across a PDF download of a series of scientific lectures by P. G. Tait from 1876 which includes a detailed review and exposition on the Carnot cycle that explains the cycle in terms of its original context as applied to STEAM ENGINES.
Suppose then we have the cylinder of a steam-engine we shall dispense with the boiler altogether, because we shall, for the sake of simplicity, always make the cylinder its own boiler. Let us have in the cylinder a small quantity of water, and the piston pressed down so as to be nearly in contact with it. Suppose, then, that our piston and the sides of our cylinder are absolutely impervious to heat. That is another thing we cannot realise, but it will have important bearings when we come to consider what are the conditions of the reversibility of an engine. We shall find in fact that any loss of heat by conduction through the sides of the cylinder is fatal to the reversibility of the engine but for all that, in our theoretical reasoning we assume that the sides of the cylinder and the piston itself are perfect non-conductors of heat. We also assume that the bottom of the cylinder is a perfect conductor of heat. These of course are all suppositions which cannot be realised in practice, but they serve to give us a conceivable and extremely simple engine to theorise upon. Suppose, then, we have three stands, on anyone of which I may place this cylinder. The first of them I call A,, the second B, and the middle one C. Now, suppose A to be a body which has a certain defined temperature, S, which is to be the temperature of the boiler. This body A is supposed to be constantly supplied with heat, so as always to be kept up (whatever happens) to that particular temperature. Then, B, which is to be used as the condenser, is to be kept constantly at a definite temperature T, lower than the temperature, S, of A.
Page 102 TRANSFORMATION OF ENERGY.
The third body is to be used merely for the theory of the operation ; it has really no effect itself. It is simply a non-conductor of heat ; it is in fact a sort of second bottom to be put upon the cylinder when it is not placed either upon the boiler or the condenser. Now,we can commence our operations in any order with this apparatus. The way in which Carnot did it is perhaps not the simplest, but it is historically the more important. We will commence, then, by setting the whole of this apparatus upon the hot body. The effect of this, as the bottom of the cylinder is a perfect conductor, is that the hot body begins at once to part with heat to the water inside, under the piston. The water then rises to the temperature S, and steam begins to form above it. This steam is limited in quantity by the space which is afforded for it, and by the temperature of the body. When as much steam has been formed as is consistent with these conditions, it is called saturated steam corresponding to the temperature S. Now, suppose that when things are in that condition, we allow the steam to expand or the piston to rise (the atmospheric pressure above the piston being easily neutralised by a counterpoise, especially in an imaginary engine), we could employ it to raise weights or do work of some kind or other externally. As it rises notice what takes place. The temperature remains the same as before, but more space is afforded for the formation of steam, and therefore more steam is formed, so that you go on keeping up saturated steam at the pressure corresponding to the temperature, S, of the boiler. As more steam is formed, more work is done, and more heat is absorbed from the boiler, because latent heat is required for the new steam as it is formed. Then,
TRANSFORMA TION OF ENERGY. Page103
while things are in that condition the piston having risen say midway up the cylinder put the whole upon the body C. No heat can get into the cylinder now, nor can any escape, for the contents are now completely surrounded by non-conducting bodies. In that state, however, the steam has still the temperature of the boiler. Let it still further expand, it will still do work, but now at the expense of its own heat, and therefore the contents will become colder. Let it go on expanding and doing work until it cools down to the temperature, T, of the condenser, and then, while it is in that state, shift the whole to the condenser. There will obviously be no transference of heat. While things are in that condition, suppose we spend work in forcing down the piston a certain way. In doing so we compress the steam, and the contents tend to become hotter, but cannot do so, because this body of temperature T is in contact with them
; so that part of the steam condenses, and the latent heat which it gives out is transferred to the cold body. With regard to the amount by which you must push down the piston during this part of the operation, Carnot said, push it so far that you give out to the condenser exactly the same amount of heat as you had taken from the boiler during the first stage of the expansion. That
statement, however, is incorrect, and requires modification, because Carnot argued on the assumption that heat is indestructible. Bearing in mind Carnot's notion of a cycle, we see that the amount by which the piston is to be depressed while the whole stands on the condenser, is
to be determined by the condition that when the whole is finally placed on the impervious stand, and
Page 104 TRANSFORMATION OF ENERGY.
the piston pressed home, the temperature of the contents shall be S, the temperature of the boiler. [This complete rectification of Carnot's cycle was given by James Thomson in 1849.] If this be effected, we can transfer the cylinder to the body A, and everything is in the condition from which we started, so that the operation may be repeated
as often as we please.
Now this all begins to make sense.
Of course, when you boil water there is no increase in temperature because there is a phase change!
Of course with condensation the "latent heat" that effected the change in state from liquid to gas is released when the process is reversed! This is why Carnot believed that the "Caloric" was merely "transported'.
But there is no such process of boiling and change of state in a hot air engine. No condensation, no "transport" of caloric, no "latent heat" of vaporization.