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, _T_↓{1}°. 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 _T_↓{2}°. It is now in the condition that it was when the cycle commenced. In this cycle of operations heat first entered, and then left the gas, and with this entrance or rejection of heat, the condition of the gas with respect to its power of doing work changed. We investigate this flow of heat, and the concomitant change of properties of the substance, with regard to which the flow took place, by forming the concept called _entropy_. We make the convention that when heat enters a substance the entropy of the latter increases, and when heat leaves it its entropy decreases. We call the quantity of heat entering or leaving a substance _Q_, and the temperature of the substance _T_. Then _Q_/_T_ is proportional to the change of entropy of the substance when the quantity of heat, _Q_, enters or leaves it. Now it is a fact of our experience that heat can only flow, _of itself_, from a hotter to a colder body. Consider two such bodies forming an isolated system, the temperature of the hotter one being _T_↓{2}°, and that of the colder one _T_↓{1}°. Let _Q_ units of heat flow from the body at _T_↓{2}° to that at _T_↓{1}° no work being done. Then the loss of entropy of the hotter body is _Q_/_T_↓{2}°, and the gain of entropy of the colder body is _Q_/_T_↓{1}°. The nett change of entropy of the system is _Q_/_T_↓{1}° - _Q_/_T_↓{2}°. Since _T_↓{2}° is greater than _T_↓{1}°, _Q_/_T_↓{2}° is less than _Q_/_T_↓{1}°. Therefore the expression _Q_/_T_↓{1}° - _Q_/_T_↓{2}° is positive, that is, the entropy of the system, as a whole, has increased. When heat flows from a hotter to a colder body the nett entropy of the two bodies, therefore, increases.