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 _T_↓{2}° to _T_↓{1}°. 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, _Q_↓{2}, from the source and gives up another quantity of heat, _Q_↓{1}, to the refrigerator. We find that _Q_↓{2} is greater than _Q_↓{1} and the balance, _Q_↓{2} - _Q_↓{1}, 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, _Q_↓{1}, is taken from the refrigerator at a temperature _T_↓{1}°, and another quantity, _Q_↓{2}, is given up to the source at a temperature _T_↓{2}°. But _Q_↓{2} is greater than _Q_↓{1}, 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