Page 45 - Entrophy Analysis in Thermal Engineering Systems

36 Entropy Analysis in Thermal Engineering Systems

Understanding reversible processes

Proof of Carnot corollaries

Carnot efficiency obtained based on
the second corollary

Kelvin temperature scale in relation
to Eq. (3.6)

Clausius inequality

Entropy
Fig. 3.3 The process of teaching entropy in thermodynamic classes.

3.3 A proposed method

The method to be proposed as an alternative to the present way of
teaching entropy relies primarily on the original Clausius approach [9].
The first step after presenting the Clausius and Kelvin-Planck statements
of the second law is to introduce the operation of the Carnot cycle on a
p-V diagram and to derive its efficiency with an ideal gas as the working
substance.

3.3.1 Derivation of the Carnot efficiency
As shown in Fig. 3.4, the Carnot cycle consists of adiabatic compression
(1!2), isothermal heating (2!3), adiabatic expansion (3!4), and iso-
thermal cooling (4!1). To derive an expression for the efficiency of the
Carnot cycle, the amount of heat transferred to the cycle at temperature
T H and that rejected by the cycle to the low-temperature reservoir at tem-
perature T L are determined using the first law.
For the isothermal expansion of an ideal gas dU¼0, the first law equation
reduces to

(3.10)
δQ ¼ δW