*3.14. Theorem C I I* |→ *C*0

**Proof.** Based on (25) and (13) we can see that {*CII*} = {*C*0}, so in particular also {*CII*} ⊂ {*C*0}. Thus, on the basis of the models (sets of processes), the considered implication holds (and even equivalence).

However, we will show directly that the *CII* principle applied to the ↓→↓ (*q*1, *w*, *q*2) engine process leads to the Carnot efficiency condition:

$$\frac{-q\_1}{T\_1} + \frac{q\_2}{T\_2} \ge 0 \quad \Rightarrow \quad \frac{-T\_2}{T\_1} \ge \frac{-q\_2}{q\_1} \quad \Rightarrow \quad 1 - \frac{T\_2}{T\_1} \ge 1 - \frac{q\_2}{q\_1} \quad \Rightarrow \quad \eta\_C \ge \eta. \tag{34}$$

Since the Carnot principle applies essentially to engine processes, the proof of formal implication may be limited here to such processes. On the other hand, the generality of the proof is additionally secured by the equality of the models.
