Physical Chemistry , 1st ed.

process spontaneous?” We will introduce and develop the tools in this chapter,

and consider a very specific answer to the question in the next chapter.

3.3 The Carnot Cycle and Efficiency

In 1824, a French military engineer named Nicolas Leonard Sadi Carnot (his

third name is borrowed from a Persian poet, and his surname is pronounced

kar-NO) published an article that ultimately played a major—though round-

about—role in the development of thermodynamics. It was ignored at the

time. The first law of thermodynamics had not even been established yet, and

heat was still thought of as “caloric.” It was not until 1848 that Lord Kelvin

brought the attention of the scientific world to the work, 16 years after Carnot’s

early death at age 36. However, the article introduced a lasting concept, the de-

finition of the Carnot cycle.

Carnot was interested in understanding the ability of steam engines—

known for almost a century by that time—to perform work. He was apparently

the first to understand that there was a relationship between the efficiencyof a

steam engine and the temperaturesinvolved in the process. Figure 3.1 shows a

modern diagram of how Carnot defined an engine. Carnot realized that every

engine could be defined as getting heat,qin, from some high-temperature

reservoir. The engine performed some work,w, on the surroundings. The en-

gine then disposed of the leftover heat in a reservoir that has some lower

temperature. The engine is therefore emitting some heat,qout, into the low-

temperature reservoir. Although the engines of today are much different

from those of Carnot’s time, every device we have for performing work can be

modeled in this fashion.

Carnot proceeded to define the steps for the operation of an engine in such

a way that the maximum efficiency could be achieved. These steps, collectively

called the Carnot cycle,represent the most efficient way known to get work out

of heat, as energy goes from a high-temperature reservoir to a low-temperature

reservoir. The engine itself is defined as the system, and a schematic of the

68 CHAPTER 3 The Second and Third Laws of Thermodynamics

Engine

System

High-temperature

reservoir, T 1

Surroundings

Supplies heat, qin,  0

Does work, w 1 ,  0

Low-temperature

reservoir, T 2

Emits heat, qout,  0

Figure 3.1 A modern diagram of the type of engine that Carnot considered for his cycle. The

high-temperature reservoir supplies the energy to run the engine, which produces some work and

emits the remainder of the energy into a low-temperature reservoir. The values ofqin,w 1 , and

qoutare greater or less than zero with respect to the system.