The Clausius inequality

Before talking about entropy, easily the most confusing aspect of engineering thermodynamics, it’s important to get clear what the Clausius inequality is. Here, again, I insist that heat transfers into a system will be taken as positive and those in which heat leaves a system are negative in value (these I label eg dQ(-)  ).

clausx claus2

Proof that V2/V1=V3/V4 for the Carnot cycle

As stated in an earlier section, here is the required proof. I’ve often seen this ‘left as an exercise for the reader’.  Such exercises are fine -once you understand the material but not as part of the explanation. One danger is that those who are less fluent with mathematical techniques are left wondering where all this stuff comes from…

volrat1 volrat2

A note on sign conventions

One thing to note about the last section is the potential for confusion in connection with the signs of Qs. My recommended approach is described below.

note on sign convention