I was under the impression that the entropy reduction in a system only works with either mass or heat transfer.

While I was researching intercooling of compressors I stumbled across a peculiar sketch (Figure 8-46 from Çengel: Introduction to Thermodynamics and Heat Transfer). I cross-checked with my thermodynamics textbook (Figure 9-43 from Çengel: Thermodynamics - An Engineering Approach).


The entropy gets smaller throughout the complete compression process. While I do understand that it gets smaller when cooled I do not understand why the entropy reduces prior and after the intercooling. Figure 9-43 shows the compression as isentropic (which is often done to simplify the analysis).

What am I missing? The only idea would be a heat-loss during the compression. I then realised that a bit later in the book a similar graph shown in Fig. 7-34:

enter image description here

What is the reason for a reduction in entropy other that heat-loss in these cases? Is it maybe a didactic choice?

  • 1
    $\begingroup$ If you induce/allow positive heat transfer to the cooler surroundings, you can decrease the entropy of a system even if its temperature is increasing. In other words, it's possible for the decrease in entropy resulting from the smaller volume to exceed the increase in entropy resulting from the higher temperature. Again, heat transfer out of the system is a requirement. I'm not sure if this answers your question? $\endgroup$ Commented Jan 14, 2018 at 0:51
  • $\begingroup$ so then it might be a didactic choice by Çengel. $\endgroup$
    – rul30
    Commented Jan 14, 2018 at 10:19

1 Answer 1


\begin{equation} {\displaystyle \Delta S=nC_{v}\ln {\frac {T}{T_{0}}}+nR\ln {\frac {V}{V_{0}}}.} \end{equation} Snipped from Entropy: wikipedia.

See also 5.4 Entropy Changes in an Ideal Gas, which I recommend you read starting at Section 5. It's taken from some of MIT's online resources.

As Chemomechanics says in his coments, the necessary condition is that there is enough heat loss from the fluid during compression such that the volume term decreases by more than the temperature term increases.

  • $\begingroup$ Ok, thanks so it seems I got the thermodynamics right. $\endgroup$
    – rul30
    Commented Jan 14, 2018 at 15:08

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