6. Entropy and the Second Law of Thermodynamics
6.9 The second law of thermodynamics for open systems
Entropy can be transferred to a system via two mechanisms: (1) heat transfer and (2) mass transfer. For open systems, the second law of thermodynamics is often written in the rate form; therefore, we are interested in the time rate of entropy transfer due to heat transfer and mass transfer.
where
Applying the entropy balance equation,
- General equation for both steady and transient flow devices
- For steady-state, steady-flow devices,
; therefore,
- For steady and isentropic flow devices,
and ; therefore,
where

Example 1
The diagrams in Figure 6.9.e1 show a reversible process in a steady-state, single flow of air. The letters i and e represent the initial and final states, respectively. Treat air as an ideal gas and assume ΔKE=ΔPE=0. Are the change in specific enthalpy Δh=he−hi, specific work w, and specific heat transfer q positive, zero, or negative values? What is the relation between w and q?

Solution:
The specific work can be evaluated mathematically and graphically.
(1) Mathematically,
(2) Graphically, the specific work is the area under the process curve in the
In a similar fashion, the specific heat transfer can also be evaluated graphically and mathematically.
(1) Graphically,
For a reversible process, the area under the process curve in the
(2) The same conclusion,
For a reversible process,
The change in specific enthalpy can then be evaluated. For an ideal gas,
Now, we can determine the relation between
In this reversible process, the specific heat transfer and specific work must be the same. Graphically, the two areas under the

Practice Problems
Media Attributions
- Entropy transfers and entropy generation through a C.V. © Pbroks13 is licensed under a Public Domain license
An isentropic process refers to a process that is reversible and adiabatic. The entropy remains constant in an isentropic process.