A new property of state: entropy

Here I show how the Clausius inequality points towards a new property of state: S

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(-)  ).

When an engine runs between T1 and T2, ht from T2 to T1 is impossible

This is an important result to establish before we confirm which Temperature, T1 or T2,  is ‘higher’.

Why can’t we have a 100%-efficient engine?

Even in an idealised, reversible cycle, some heat must be rejected. The Second Law implies there is a limit to the thermal efficiency of cyclic engines.

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…

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.