1st and 2nd laws are fundamental unifying principles of thermodynamics

Energy is conserved

Heat is a form of energy transfer

Restrictions on the energy transfer

Kelvin statement of the second law:

Second Law of Thermodynamics

There is no process whose only effect is to accept heat from a single heat reservoir and transform it entirely into work.

Clausius statement of the second law:

There is no process whose only effect is to accept heat from a colder reservoir and transform it to a hotter one.

Lord Kelvin (William Thomson) (1824-1907)

Rudolf Clausius (2.1.1822 -24.8.1888)

Hypothetical devices violating the 2nd Law

Alternative Kelvin statement:

Note the careful wording:

Kelvin statement of the second law:

There is no process whose only effect is to accept heat from a single heat reservoir and transform it entirely into work.

x

T=const

V

V0V~V~d

nRTW

0V

VlnnRT

V

Why is this no contradiction

Because: Transformation of heat work is not the only effect (piston moved)

inQ

Note: In a cyclic process engine remains unchanged only

Clausius statement of the second law:

There is no process whose only effect is to accept heat from a colder reservoir and transform it to a hotter one.

Again: A refrigerator accepts heat from a colder reservoir and transfers heat to the hotter reservoir

Why is this no contradiction

Because: This is not the only thing a refrigerator does. It uses electrical or mechanical energy.

Alternative Clausius statement

Michael Flanders and Donald Swan

The First Law of Thermodynamics:Heat is work and work is heat.Very good!

The Second Law of Thermodynamics:Heat cannot of itself pass from one body to a hotter body.Heat won’t pass from a cooler to a hotter.You can try it if you like, but you far better notter,Cause the cold in the cooler will get hotter as a ruler,Cause the hotter body’s heat will pass to the cooler.First law: Heat is work and work is heat.Heat will pass by conduction,And heat will pass by convection,And heat will pass by radiation,And that’s a physical law.Heat is work and work’s a curse,And all the heat in the universe is gonna to cool down,Cause it can’t increase,And then there’ll be no more work and there’ll be perfectpeace.Really!Yeah, that’s entropy man.And all because of the second law of thermodynamics whichlays down that:You can’t pass heat from a cooler to a hotter.You can try it if you like, but you’d far better notter,Cause the cold in the cooler will get hotter as a ruler,Cause the hotter body’s heat will pass to the cooler.And that’s a physical law.Ooh, I’m hot!Hot! That’s because you’ve been working!That’s the first and second law of thermodynamics.

We show with the help of the Kelvin statement that:

All 2-temperature engines accept heat at the hotter reservoir and reject heat at the colder reservoir

Indirect proof:

Contradiction of

(*)

(*): There is at least one 2-temperature engine which acceptsheat from the colder reservoir and rejects heat to the hotter reservoir

Tc

Th

W

Test engine

testhQ

Copperrod

rodhQ =

e.g., by adjusting copper rod

Let’s call it test engine

Tc

Th

W

Test engine

testhQ

Copperrod

rodhQ =

e.g., by adjusting copper rod

Q T

W

Non-Kelvindevice

Since the Kelvin statement rules out the possibility of the device

Q T

W

Contradiction of (*) False

(*) trueAll 2-temperature engines accept heat at the hotter reservoir and reject heat at the colder reservoir

Equivalence of the Clausius and Kelvin statements

Logical structure of the proof of equivalence:

1

2

possibility I

Kelvin-statement

Clausius-statement

true

true

II

false

true

III

true

false

IV

false

false

We show:

Kelvin-statement false Clausius-statement false

Clausius-statement false Kelvin-statement false

The decision between possibility I and IV is made by experimental experience

1 Kelvin-statement false

Clausius-statement false

There is a non-Kelvin engine

Let’s combine this non-Kelvin engine with a heat pump (which we know to exist)

There is a non-Clausius engine

2 Clausius-statement false

Kelvin-statement false

There is a non-Clausius engine

Let’s combine this non-Clausius engine with a heat engine (which we know to exist)

There is a non-Kelvin engine

Q

Q

QQ

Q