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1. Second Law of Thermodynamics Restrictions on the energy transfer Hypothetical devices violating the 2nd Law Lord Kelvin (William Thomson) (1824-1907) Rudolf Clausius (2.1.1822 -24.8.1888) 1st and 2nd laws are fundamental unifying principles of thermodynamics Energy is conserved Heat is a form of energy transfer 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. 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.

2. Alternative Kelvin statement: x 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. T=const Why is this no contradiction work is not the only effect (piston moved) Because: Transformation of heat In a cyclic process engine remains unchanged Note: only

3. Alternative Clausius statement 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.

4. 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 perfect peace. Really! Yeah, that’s entropy man. And all because of the second law of thermodynamics which lays 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.

5. 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 Let’s call it test engine Indirect proof: (*): There is at least one 2-temperature engine which accepts heat from the colder reservoir and rejects heat to the hotter reservoir Contradiction of = e.g., by adjusting copper rod Th Test engine Copper rod Tc

6. = e.g., by adjusting copper rod Th Test engine Copper rod Tc T Non-Kelvin device T Since the Kelvin statement rules out the possibility of the device (*) False Contradiction of All 2-temperature engines accept heat at the hotter reservoir and reject heat at the colder reservoir true (*)

7. Equivalence of the Clausius and Kelvin statements Logical structure of the proof of equivalence: I II III IV possibility Kelvin-statement true false true false Clausius-statement true true false false We show: Kelvin-statement false Clausius-statement false 1 Clausius-statement false Kelvin-statement false 2 The decision between possibility I and IV is made by experimental experience

8. Kelvin-statement false There is a non-Kelvin engine 1 Let’s combine this non-Kelvin engine with a heat pump (which we know to exist) Clausius-statement false There is a non-Clausius engine

9. Clausius-statement false There is a non-Clausius engine 2 Let’s combine this non-Clausius engine with a heat engine (which we know to exist) Kelvin-statement false There is a non-Kelvin engine