Conversion of Heat to Work (a heat engine)
Heat reservoir at
temperature T2 > T1
Q  heat
W  work
both in Joules
Q2
Heat
Engine
Q1
Cold reservoir at
temperature T1 < T2
W
Cooling via Work (Carnot Refrigerator)
Environment at
temperature Th > Tl
Qh
W
Refrigerator
Ql
Ql
 R  Ql / W 
Qh  Ql
Tl

Th  Tl
Refrigerator, inside
temperature Tl < Th
Carnot Heat Pump
Environment
(Home) Th > Tl
Qh
W
Heat
Pump
Ql
 HP
Qh
 Qh / W 
Qh  Ql
Th
Tl

 1
1
Th  Tl
Th  Tl
Resevoir (ground)
Tl < Th
Always > 100%
The Clausius Inequality and the 2nd Law
P
Divide any reversible cycle into a
series of thin Carnot cycles, where
the isotherms are infinitesimally
short:
đQ2

đQ1
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!
The Clausius Inequality and the 2nd Law
P
Divide any reversible cycle into a
series of thin Carnot cycles, where
the isotherms are infinitesimally
short:
đQ2

đQ1
v
For a reversible process!
Leads to the definition of
entropy for a reversible
process:
đQr
dS =
T
The Clausius Inequality and the 2nd Law
P
Divide any reversible cycle into a
series of thin Carnot cycles, where
the isotherms are infinitesimally
short:
đQ2

đQ1
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.