Ultimate Fate of The Universe

Hello Steemians
Let me tell you why you don't need to clean your room frequently.

Heat flows from a hot body to a cold body, dye mixes uniformly in water, an object tries to be in minimum energy state etc. unless we don't interfere with the system. It seems that nature is trying to distribute energy equally to all the systems. From this examples, we know that the energy in chunk form tries to be distributed among system and the surrounding. This phenomenon is known as entropy.

(https://phys.org/news/2015-09-fate-universeheat-death-big-rip.html)

Let me start with a famous definition, "Entropy is the measure of the degree of randomness". It is known that entropy is a physical quantity cause it measures some phenomena. Randomness means the possibility of different states. Molecules in an ice have a lesser possibility of states but in gas, the molecules are in random vibration and with more possibility of states. So, we can say the entropy of the gas is more than that of ice. In cold body, the molecular vibration and possibility is less than that in the hot body. So, the entropy of hot body is more than that of a cold body.

From these two paragraphs, we know that nature acts such that a system with lower entropy gains the entropy. We can now check the feasibility or spontaneity of the process using entropy. If entropy increases, the process is spontaneous and if not, the process is non-spontaneous.

Entropy can only increase over time for an isolated system. It is second law of thermodynamics.

dS ≥ 0

Thermodynamically,

dS = dQ/T

dQ = Heat change in the system
dS = Change in entropy
T = Absolute temperature of the system.

Let there be two reservoirs A and B with temperatures T1 and T2(T1 > T2) respectively and let T be the temperature of the atmosphere.
If we extract Q amount of heat from reservoir A. The maximum amount of heat that can be extracted from two temperature is by operating it under Carnot cycle. It is given by;

W1 = η Q
η is efficiency.
η = (1 - T/T1)
So, W1 = (1- T/T1)Q

Now Q amount of heat is transferred from reservoir A to reservoir B. This is a spontaneous process(T1>T2). Then, the work extractable from reservoir B is

W2 = (1- T/T2) Q
There will be a decrease in potential extractable work due to spontaneous process in the intermediate.

E = W1 - W2

E = (1- T/T1)Q - (1- T/T2)Q

E = (T/T2 - T/T1) Q

E = T(Q/T2 - Q/T1)

E = T(ΔSb + ΔSa)

E = T ΔS

It is for the irreversible heat transfer process.

Spontaneous processes occur every time in nature and all these processes increase the entropy of the universe. The extractable work will go on decreasing. Ultimately, entropy reaches a maximum and extractable work will be zero which will lead to the thermal equilibrium of the universe. It is called heat death of the universe. And at last, during any mechanical work you are increasing the entropy of the universe. So, it is recommended to clean your room less frequently . :p

Sources:

i. ocw.mit.edu

ii. Concept of Physics

iii. Balakrishan Lecture, NPTEL

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