Second law and entropy practice problems
The second law of thermodynamics deals with thermal machines. The following is a common representation of a heat engine, a machine that receives heat from a hot reservoir, produces work and then transfers some heat to a colder reservoir.
Heat engine
The opposite would be called a refrigerator: it’s the mechanism that you find in the fridge you have in your kitchen. The machine does some work (in the case of a fridge, by using electrical energy), it takes heat from a cooler body and it transfers it to a hotter reservoir (the environment).
Efficiency is defined like this, where $\eta$ is the efficiency of the machine, **$W$ **is the work and $Q_h$ is the heat coming from the hot reservoir ⬇️
$$ \eta = \frac{W}{Q_h} $$
Since $W = Q_h-Q_c$ because of the principle of conservation of energy, we can also write the definition above like below ⬇️
$$ \eta = 1 - \frac{Q_c}{Q_h} $$
This formula highlights the fact that the efficiency of a machine is always strictly between 0 and 1: $0<\eta<1$.
A transformation is said reversible when the system and its environment can be taken back to their initial state carrying out the transformation in reserve. No real transformation is reversible, however this concept will be useful in this chapter.
All transformations in thermodynamics are considered quasi-static. Quasi means “almost”, so quasi-static means “almost static”. The meaning of this is that transformations in thermodynamics are considered to happen so slowly that each time the gas changes its state, it passes from a state of equilibrium to another state of equilibrium, without additional steps.
There are a lot of ways to state the second law of thermodynamics, let’s see each of them one by one.