# Explain why the entropy of the universe increases in all real processes?e

Arun
25750 Points
5 years ago
Mathematical explanation:
Entropy is the ratio of measurable heat change and the absolute temperature, i.e., ΔS=ΔQ/T= (ΔQ) ÷ T

Consider the two different kinds of processes:
1. Reversible process (All intermediates states are in equilibrium):
Let the system absorb heat 'q' from its surroundings.
ΔS(system)=(+q)/T
ΔS(surroundings)= (-q)/T
[Note that the temperatures of both remain same, as there is a constant equilibrium state. Minus sign indicates loss of heat.]
ΔS(total)=ΔS(system)+ΔS(surroundings)=0

2. Irreversible process: Consider the system at a higher temperature T1 and the surroundings at a lower temperature T2. Since heat flows from a system at higher temperature to a system at lower temperature in an irreversible, natural process. If the system loses heat q to the surroundings,
ΔS(system)=(-q)/T1
ΔS(surroundings)= (+q)/T2
ΔS(total)=ΔS(system)+ΔS(surroundings)={q (T1-T2)} ÷ T1T2
Since T1>T2, therefore, T1-T2>0
Therefore, ΔS(process)>0

Hence, whichever process may take place, the system shall always experience an increase in entropy. (Note that the reversible reactions don't add to entropy. Most irreversible processes are favored by all laws and they increase stability.)

Theoretical explanation:
Entropy is simply a mathematical manifestation of disordering. In other words, at a particular temperature, the extent of disordering is explained by entropy (this explains the term ΔQ in the formula). At higher temperature, the same change of heat (ΔQ) causes lesser disordering (this explains inverse variation of ΔS with T). Any feasible and spontaneous process causes disorder in the previous configuration and hence, the entropy increases.
For instance, on connecting two flasks, one of which contains a gas and the other is empty, we find that the molecules of the gas have occupied both flasks to achieve a more probable distribution and entropy increases. Such a probability distribution, by default, is the most observed and hence, more stable.