Question

For each of the following irreversible processes, explain how you can tell that the total entropy of the universe has increased.
$\left(a\right)$ Stirring salt into a pot of soup.
$\left(b\right)$ Scrambling an egg.
$\left(c\right)$ Humpty Dumpty having a great fall.
$\left(d\right)$ A wave hitting a sand castle.
$\left(e\right)$ Cutting down a tree.
$\left(f\right)$Burning gasoline in an automobile.

Short answer

Part $\left(a\right)$

$\left(a\right)$Stirring salt into a pot of soup - The entropy is related to the natural logarithm of the multiplicity, thus more configurations equals more multiplicity.

Part $\left(b\right)$

$\left(b\right)$Scrambling an egg - This process cannot be reversed the more they are arranged than when they are apart.

Part $\left(c\right)$

$\left(c\right)$Humpty Dumpty having a great fall - When it hits the ground, it splits into fragments, the configurations of which are huge, increasing the variety, and the entropy grows as well.

Part $\left(d\right)$

$\left(d\right)$A wave hitting a sand castle - The amount of ways the sand bits may be removed from the castle is enormous.

Part $\left(e\right)$

$\left(e\right)$Cutting down a tree - Choose any location to cut, as well as a variety of angles, to give it a variety of ways to fall; the range of things to fall is far more than when it is standing.

Part $\left(f\right)$

$\left(f\right)$Burning gasoline in an automobile - Because gasoline breaks down into little gas molecules, the number of molecules will rise, and the creation of heat will also increase the entropy.

Step-by-step solution

Step: 1 Definition of irreversible process in entropy:

The entropy of the cosmos remains unaltered in a reversible process, whereas the entropy of the universe grows in an irreversible process. It also rises when a quantifiable non-spontaneous process occurs. Because energy continually goes downward, entropy increases.The overall energy of the system and its environment grows when an irreversible event occurs.

Step: 2 Total entropy of the universe has increased reasons: (part a and b)

Stirring salt into a pot of soup - Once you mix a salt into a pot of soup, the sodium and chlorine molecules dissolve in the soup, resulting in more configurations than when they're confined in a crystal. The entropy is related to the natural logarithm of the multiplicity, thus more configurations means more multiplicity. Reversing the procedure and removing the salt from the soup is difficult.

Scrambling an egg - Scrambling an egg causes the white and yolk to combine, resulting in more arrangement than when they are separated; furthermore, this process is irreversible.

Step: 3 Total entropy of the universe has increased reasons: (part c and d) 

Humpty Dumpty having a great fall - If we ignore air resistance, we may consider Humpty Dumpty's fall to be reversible. However, when it hits the ground, it splits into pieces, the configurations of which are huge, resulting in multiplicity, and entropy grows as the multiplicity increases.

A wave hitting a sand castle - Once the wave hits the sand castle, it causes the sand bits to be taken from the castle in a variety of ways, resulting in a high level of entropy.

Step: 4 Total entropy of the universe has increased reasons: (part e and f) 

Cutting down a tree - As we cut the tree, we may select any location to cut it, as well as different angles, giving it a variety of ways to fall. Entropy grows as a result.

Burning gasoline in an automobile - When gasoline is burned in a car, the number of molecules rises because the gasoline breaks down into little gas molecules. Additionally, the creation of heat increases the entropy of the environment surrounding the burning site, resulting in an increase in entropy.