Page 37 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch03 Elementary Physical Chemistry

22 Elementary Physical Chemistry

the statement is usually expressed in the form of two equivalent Principles:

Claussius Principle: It is not possible to construct an engine
which has the sole effect of transferring heat from a lower temper-
ature reservoir to a higher one.

or,
Kelvin–Planck Principle: It is not possible to construct an
engine which has the sole effect of converting heat entirely into
work.

It can be shown that either statement leads to the conclusion that dq rev /T
is path-independent and this statement is used to define entropy. It can be
shown also rigorously that statements (3.3)–(3.6) are valid.

3.2. Carnot Cycle
The standard way of proving the foregoing statements is by means of a
Carnot cycle. This is a reversible cycle consisting of an isothermal expansion
of a gas from a volume V 1 toavolume V 2 at a temperature T 2 , followed
by an adiabatic (no heat transfer) expansion of the gas from V 2 to V ,then

2
followed by an isothermal compression from V to V at a temperature T 1 ,

2 1
and finally followed by an adiabatic compression from V to V 1 .

1
The system (gas) is connected to an engine, consisting of two heat
reservoirs, one at the higher temperature, T 2, and the other at the lower
temperature, T 1 (see Figs. 3.1 and 3.2). The heat, q 2 , extracted from the
high temperature reservoir T 2 is used to run the Carnot cycle, thereby
generating work, −w, and returning the remaining heat q 1 to the reservoir
at the lower temperature T 1 .[Note: q 2 and q 1 are symbolic representations:
q 2 is positive, and q 1 is negative. Work done on the surrounding has a
negative sign because we use the convention that w represents the work
done by the surrounding on the system, and thus the work done by the
system must be −w.]

3.3. Engine Efficiency
The efficiency, ξ, is defined as the work done by the system in a complete
cycle divided by the heat absorbed at the higher temperature, i.e.

(3.7)
ξ = −w/q 2