Physical Chemistry Third Edition

3.1 The Second Law of Thermodynamics and the Carnot Heat Engine 107

(b)

Working fluid

(system)

Piston

Hot

reservoir

Cold

reservoir

Connecting

rod

Crankshaft

(a)

Intake

valve

Steam

inlet

Steam

exhaust

Exhaust

valve

Piston

Connecting

rod

Crankshaft

Figure 3.1 Comparison of a Simple Steam Engine and a Carnot Engine (Schematic).

(a) A Simple steam engine. (b) A Carnot heat engine.

valve open. High-pressure steam from the boiler enters the cylinder through the intake

valve and pushes on the piston, which turns the crankshaft. When the piston reaches

bottom dead center (the position of maximum volume in the cylinder) the intake valve

closes and the exhaust valve opens. The inertia of the crankshaft and flywheel pushes

the piston back toward top dead center, expelling the spent steam through the exhaust

valve. The exhaust valve closes and the intake valve opens when top dead center is

reached, and the engine is ready to repeat its cycle.

The Carnot engine is depicted in Figure 3.1b. It operates reversibly, so there can

be no friction. The cylinder contains a gaseous “working fluid,” which we define to

be the system. The Carnot engine has no valves and the system is closed. To simulate

passing steam into and out of the cylinder the Carnot engine allows heat to flow from

a “hot reservoir” into its working fluid and exhausts heat into a “cold reservoir” by

conduction through the cylinder walls or cylinder head.

The Carnot engine operates on a two-stroke cycle that is called theCarnot cycle.We

begin the cycle with the piston at top dead center and with the hot reservoir in contact

with the cylinder. We break the expansion stroke into two steps. The first step is an

isothermal reversible expansion of the system at the temperature of the hot reservoir.

The final volume of the first step is chosen so that the second step, which is an adiabatic

reversible expansion, ends with the system at the temperature of the cold reservoir and

with the piston at bottom dead center. The compression stroke is also broken into two

steps. The third step of the cyclic process is a reversible isothermal compression with