# Equivalence of two statements:

Mechanics

Oct 27, 2013 (4 years and 8 months ago)

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THE SECOND LAW OF THERMODYNAMICS
Kelvin – Planck Statement: It is impossible for any device that operates on a cycle
to receive heat from a single reservoir and
produce a net amount of work
For heat engine to operate, the working fluid has
to exchange heat with heat sink as well with the heat source.

If
L
Q 0
=
, then
L
th
H
Q
1 1
Q
η
= − =
, therefore, the 2
nd
law claims that
no heat engine can be
100%
efficient:

Clausius Statement: No device can operate on a cycle and produce effect
that is solely the heat transfer from
a lower-temperature body to a higher-temperature body

There are devices that can transfer heat
from lower-temperature reservoirs to higher-temperature reservoirs
but they have also to consume some energy W
in

Equivalence of
two statements:
If some device
violates one statement,
it also violates
the other statement,
and vice versa.

H
T
Heat
Engine
net,out
W
H
Q
th
< 1
η

L
T

H
T
H
Q
L
Q
2) Attach heat engine to refrigerator
3) Violation of Clausius statement
1) Assume that Kelvin-Planck statement i
s violated

L
T

H
T
H out
Q =W
H
Q
th
Heat
Engine
1
η
=

L
T

H
T
H L
Q Q
+
L
Q
H in
Q =W
H
Q
th
Heat
Engine
1
η
=
Refrigerator

L
T

H
T
L
Q
L
Q
combine in a single device
Lord Kelvin
(1824-1907)
Max Planck
(1858-1947)
Rudolf Clausius
(1822-1888)
nd
Violation
of the 2 law:
nd
Violation
of the 2 law: