CHAPTER 4 THE SECOND LAW
4.2 STATEMENTS OF THESECONDLAW 103
(a)coolqwarm(b)coolqdeviceqwarmFigure 4.1 Two impossible processes in isolated systems.
(a) Heat transfer from a cool to a warm body.
(b) The same, with a device that operates in a cycle.an equal quantity of heat should flow from the device to the warm body, and the final state
of the device should be the same as its initial state. In other words, we want the device to
transfer energy quantitatively by means of heat from the cool body to the warm body while
operating in acycle. If the device could do this, there would be no limit to the quantity of
energy that could be transferred by heat, because after each cycle the device would be ready
to repeat the process. But experience shows thatit is impossible to build such a device! The
proposed process of Fig.4.1(b) is impossible even in the limit of infinite slowness.
The general principle was expressed by Rudolph Clausius^2 in the words: “Heat can
never pass from a colder to a warmer body without some other change, connected there-
with, occurring at the same time.” For use in the derivation to follow, the statement can be
reworded as follows.
The Clausius statement of the second law: It is impossible to construct a device whose
only effect, when it operates in a cycle, is heat transfer from a body to the device and
the transfer by heat of an equal quantity of energy from the device to a warmer body.
Next consider the impossible process shown in Fig.4.2(a) on the next page. A Joule
paddle wheel rotates in a container of water as a weight rises. As the weight gains potential
energy, the water loses thermal energy and its temperature decreases. Energy is conserved,
so there is no violation of the first law. This process is just the reverse of the Joule paddle-
wheel experiment (Sec.3.7.2) and its impossibility was discussed on page 66.
We might again attempt to use some sort of device operating in a cycle to accomplish
the same overall process, as in Fig.4.2(b). A closed system that operates in a cycle and
does net work on the surroundings is called aheat engine. The heat engine shown in Fig.
4.2(b) is a special one. During one cycle, a quantity of energy is transferred by heat from
a heat reservoir to the engine, and the engine performs anequalquantity of work on a
weight, causing it to rise. At the end of the cycle, the engine has returned to its initial
state. This would be a very desirable engine, because it could convert thermal energy into
an equal quantity of useful mechanical work with no other effect on the surroundings.^3 The
(^2) Ref. [ 32 ], page 117.
(^3) This hypothetical process is called “perpetual motion of the second kind.”