The Second Law of Thermodynamics
Laws
Clausius: There is no process that transfers heat from a colder body to a hotter body by itself.
Kelvin: A process that converts all heat into work is impossible.
Explanation
The statements by German physicist Clausius and British physicist Kelvin on the Second Law of Thermodynamics are equivalent to each other. The most famous version is by the Greek mathematician Carathéodory, stating that ’the entropy of a closed system does not decrease’. This is popular especially among laypeople because it affirms eschatology without using terms like ‘hot’ or ‘work,’ thus sounding sophisticated. It’s a concept often cherry-picked by those who, without serious consideration, prefer pseudoscience, like ‘Schrodinger’s cat’. Let’s define the terms mentioned in the laws more precisely for a better explanation.
Colder means having a relatively lower [temperature].
Hotter means having a relatively higher temperature.
The conversion of [heat] into work is referred to as a process.
A closed system that receives heat from outside to perform a process is called a heat engine.
Let’s say a heat engine receives heat $Q_{h}$ and does work $W$. Then, $\eta : = \dfrac{W}{Q_{h}}$ is referred to as efficiency.
Steam engines and hot air balloons are examples of heat engines. Efficiency is logically defined as the ‘ratio of energy converted into desired work out of the total energy provided to the engine’.
Using blue for colder with $l$ and red for hotter with $h$, we can illustrate it as above, showing the energy received at a higher temperature and the remaining energy after some of it is used for work.
Clausius: There is no process that transfers heat from a colder body to a hotter body by itself
The diagram above schematically represents Clausius’s Second Law of Thermodynamics. Simply put, Clausius’s statement implies ‘heat always flows from a higher place to a lower one’. If this law were incorrect, water could flow uphill, and suddenly heat could appear out of nowhere, warming things up.
Of course, if a machine receives work from the outside as shown above, the story changes. Since it’s not a process where heat is ‘spontaneously’ transferred from a colder to a hotter body, heat has been transferred from cold to hot. This does not violate the Second Law of Thermodynamics because the assumption of a ‘closed system’ was not met, making it possible.
Kelvin: A process that converts all heat into work is impossible
The diagram above schematically represents Kelvin’s Second Law of Thermodynamics. Simply put, Kelvin’s statement means ‘it’s impossible to have no loss’. If this law were incorrect, Galileo’s thought experiment would have been a real experiment, and perpetual motion machines would exist.