Third operation, (3→4). But the piston is not at the lower end of its stroke yet. We turn the valve so that the bottom of the cylinder is closed by the non-conducting plug O, and then push in the piston until it reaches the position III. The gas is still further compressed, and this compression generates heat. But the heat cannot escape, so that the temperature of the gas rises until it reaches T2°. The contraction is therefore an adiabatic one. Work is done on the gas.
Fourth operation, (4→1). The piston is now at the lower end of its stroke. We turn the valve so that the bottom of the cylinder is placed in communication with the source of heat (+). The gas expands from the point beneath 4 to the point beneath 1, raising the piston to the position II. This expansion of the gas would lower its temperature, but it is in communication with the source of heat, and so it does not cool, but draws heat from the source and remains at a constant temperature, T2°. The expansion is therefore an isothermal one. Work is done by the gas.
This completes the cycle. But the gas is heated, and when the piston is at position II, the valve is turned so as to close the cylinder by the non-conducting plug O. The heat already contained in the gas continues to expand, the latter doing more work, but this expansion causes the temperature to fall from T2° to T1°. This is the operation with which the cycle commenced.
Summarising the positive Carnot cycle, we see that the engine takes heat from a source (+) and gives up part of this to a refrigerator (−), (in an actual steam-engine heat is taken from the boiler and given up to the condenser water). If we measure the quantity of heat taken from the boiler in the steam which enters the cylinders we shall find that this quantity of heat is greater than the quantity which is given up to the condenser water. What becomes of the balance? It is converted into the mechanical work of the engine. The Carnot engine therefore takes a quantity of heat, Q2, from the source and gives up another quantity of heat, Q1, to the refrigerator. We find that Q2 is greater than Q1 and the balance, Q2 − Q1, is represented by the work done by the engine. Heat-energy falls from a state of high, to a state of low potential, and is partly transformed into mechanical work.
THE CARNOT NEGATIVE CYCLE
This is simply the positive cycle reversed. The reader should puzzle it out for himself if he is not already familiar with it. It consists of an adiabatic contraction 2→1, an isothermal contraction 1→4, an adiabatic expansion 4→3, and an isothermal expansion 3→2. A quantity of heat, Q1, is taken from the refrigerator at a temperature T1°, and another quantity, Q2, is given up to the source at a temperature T2°. But Q2 is greater than Q1, and the engine therefore gives up more heat than it receives, while, further, heat flows from a body at a low temperature to another body at a higher temperature. Where does the engine get this energy from? It gets it because work is done upon it by means of an outside agency, and all of this work is converted into heat.
REVERSIBILITY
The Carnot engine and cycle are therefore perfectly reversible. Not only can the engine turn heat into work, but it can turn work into heat. This perfect, quantitative reversibility is, however, a property of the imaginary mechanism only, and it does not exist in any actual engine.
ENTROPY
Let us consider the cycle more closely. In the operation 4→1, which is an isothermal expansion, there is a flow of heat-energy from the source and a transformation of energy into work. The gas in the condition represented by the point 4 had a certain pressure and a certain volume. In the condition represented by the point 1, its pressure has decreased, its volume has increased, and its temperature is the same. Its physical condition has been changed, and to bring it back into its former condition something must be done to it. Let, then, the gas continue to expand without receiving any more heat, or parting with any: that is, let it undergo the adiabatic expansion 1→2 until its temperature falls to that of the refrigerator, T1°. We now compress the gas while keeping it at this temperature, that is, we cause it to undergo the isothermal contraction 2→3, during which operation it is giving up heat to the refrigerator, so that there is again a flow of heat-energy. We then compress it still further without allowing heat to escape from it, that is, we cause it to undergo the adiabatic contraction 3→4. During this operation the gas rises in temperature to T2°. It is now in the condition that it was when the cycle commenced.