1. Conversion of Heat to Work (a heat engine)
Heat reservoir at
temperature T2 > T1
Q  heat
W  work
both in Joules Q2
Heat
Engine W Q1
Cold reservoir at
temperature T1 < T2

2. Cooling via Work (Carnot Refrigerator)
Environment at
temperature Th > Tl Qh
Refrig-
erator Ql
Refrigerator, inside
temperature Tl < Th

3. Environment (Home) Th > Tl Resevoir (ground) Tl < Th
Carnot Heat Pump
Environment
(Home) Th > Tl Qh
Heat
Pump Ql
Resevoir (ground)
Tl < Th
Always > 100%

4. The Clausius Inequality and the 2nd Law
Divide any reversible cycle into a series of thin Carnot cycles, where the isotherms are infinitesimally short: P  v
We have proven that the quantity dS = dQr/T is a state variable, since its integral around a closed loop is equal to zero, i.e. the integration of differential entropy, dS, is path independent!

5. The Clausius Inequality and the 2nd Law
Divide any reversible cycle into a series of thin Carnot cycles, where the isotherms are infinitesimally short: P  v
For a reversible process!
Leads to the definition of entropy for a reversible process:

6. The Clausius Inequality and the 2nd Law
Divide any reversible cycle into a series of thin Carnot cycles, where the isotherms are infinitesimally short: P  v
There is one major caveat: the cycle must be reversible. In other words, the above assumes only configuration work (PdV) is performed.
If the cycle additionally includes dissipative work, it is not clear how to include this in the above diagram.

7. The Clausius Inequality