THERMODYNAMICS & ENTROPY NOTES
THERMODYNAMICS & ENTROPY
Complete Core Masterclass Notes — B.Sc. Physical Sciences & Chemistry
High-Yield Study Material for Academic Excellence
# Unattainability of Absolute Zero
We know from Carnot's principle —
Q2 / Q1 = T2 / T1
Q2 = (T2 / T1) × Q1
If T2 = 0, absolute zero
Then Q2 = 0
This is not possible as no engine can fully convert 100% heat into 100% work.
Hence, by no mechanical means we can attain absolute zero.
A key consequence is that absolute zero cannot be reached, since removing heat becomes increasingly
inefficient and entropy changes vanish. This unattainability principle means no physical process can cool a
system to absolute zero in a finite no. of steps or finite time.
⇒ The most accepted version of the 3rd law of thermodynamics, the unattainability principle, states that any
process cannot reach absolute zero Temp. in a finite no. of steps and within a finite time.
# Third Law of Thermodynamics / Nernst Theorem
"Entropy of a pure crystalline substance at absolute zero temp. is zero."
Mathematically it can be stated as —
limT → 0 dS = 0
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, THERMODYNAMICS & ENTROPY NOTES
Advantages —
This law is convenient in explaining —
1. The nature of bodies in neighborhood of absolute zero temp.
2. It permits the calculation of absolute value of entropy and physical interpretation of thermodynamic properties
such as chemical and Gibbs free energies etc.
Limitations —
1. It is applicable only in case of pure compounds.
2. It is not applicable to amorphous substance.
3. It is not applicable to glassy solids.
# Entropy Change in An Isolated System
∮ dQ / T = ∫AB (dQ / T)R + ∫BA (dQ / T)I ≤ 0
∫AB dQ / T ≤ − ∫BA dQ / T
(SB − SA) ≥ ∫AB dQ / T
dS ≥ ∫AB dQ / T
For an isolated system heat transfer is zero.
i.e., dQ = 0
i.e., dS ≥ 0
# Principle of Increase of Entropy
Statement: It states that the entropy of an isolated system either increases or remains constant according as
the process is irreversible or reversible. i.e., dSisolated ≥ 0
Proof:
Here A→B follows reversible process and B→A follows in irreversible process.
From Clausius inequality —
Page 2
THERMODYNAMICS & ENTROPY
Complete Core Masterclass Notes — B.Sc. Physical Sciences & Chemistry
High-Yield Study Material for Academic Excellence
# Unattainability of Absolute Zero
We know from Carnot's principle —
Q2 / Q1 = T2 / T1
Q2 = (T2 / T1) × Q1
If T2 = 0, absolute zero
Then Q2 = 0
This is not possible as no engine can fully convert 100% heat into 100% work.
Hence, by no mechanical means we can attain absolute zero.
A key consequence is that absolute zero cannot be reached, since removing heat becomes increasingly
inefficient and entropy changes vanish. This unattainability principle means no physical process can cool a
system to absolute zero in a finite no. of steps or finite time.
⇒ The most accepted version of the 3rd law of thermodynamics, the unattainability principle, states that any
process cannot reach absolute zero Temp. in a finite no. of steps and within a finite time.
# Third Law of Thermodynamics / Nernst Theorem
"Entropy of a pure crystalline substance at absolute zero temp. is zero."
Mathematically it can be stated as —
limT → 0 dS = 0
Page 1
, THERMODYNAMICS & ENTROPY NOTES
Advantages —
This law is convenient in explaining —
1. The nature of bodies in neighborhood of absolute zero temp.
2. It permits the calculation of absolute value of entropy and physical interpretation of thermodynamic properties
such as chemical and Gibbs free energies etc.
Limitations —
1. It is applicable only in case of pure compounds.
2. It is not applicable to amorphous substance.
3. It is not applicable to glassy solids.
# Entropy Change in An Isolated System
∮ dQ / T = ∫AB (dQ / T)R + ∫BA (dQ / T)I ≤ 0
∫AB dQ / T ≤ − ∫BA dQ / T
(SB − SA) ≥ ∫AB dQ / T
dS ≥ ∫AB dQ / T
For an isolated system heat transfer is zero.
i.e., dQ = 0
i.e., dS ≥ 0
# Principle of Increase of Entropy
Statement: It states that the entropy of an isolated system either increases or remains constant according as
the process is irreversible or reversible. i.e., dSisolated ≥ 0
Proof:
Here A→B follows reversible process and B→A follows in irreversible process.
From Clausius inequality —
Page 2
