Statement (I): The Inequality of Clausius provides the criterion of the reversibility of a cycle.

Statement (II): \( \mathop \oint \nolimits \frac{{\delta Q }}{T} > 0\) the cycle is irreversible and possible

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  1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
  2. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)
  3. Statement (I) is true but Statement (II) is false
  4. Statement (I) is false but Statement (II) is true

Answer (Detailed Solution Below)

Option 3 : Statement (I) is true but Statement (II) is false
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Concept:

Entropy:

  • Entropy is the index of unavailability or degradation of energy. Heat always flows from hot bodies to cold bodies and this becomes degrades or less available.
  • For a reversible transfer of heat change in entropy

\({\rm{\Delta }}s = {s_2} - {s_1} = \mathop \smallint \nolimits \frac{{dQ}}{t}\) where, s = entropy, Q = heat, T = temperature

  • No process between two equilibrium states is possible if it would result in a decrease in the total entropy of the system and surroundings.

Clausius Inequality:

  • Clausius inequality states that \(\oint \frac{{{\rm{dQ}}}}{{\rm{T}}} \le 0\)
  • It provides the criteria for the reversibility of a cycle.
  • If \(\oint \frac{{{\rm{dQ}}}}{{\rm{T}}} = 0\), the cycle is reversible,
  • If, \(\oint \frac{{{\rm{dQ}}}}{{\rm{T}}} < 0\), the cycle is irreversible and possible
  • If \(\oint \frac{{\partial Q}}{T} > 0\), the cycle is impossible
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