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In an irreversible process taking place at constant $T$ and $P$ and in which only pressure-volume work is being done the change in Gibbs free energy ($dG$) and change in entropy ($dS$) satisfy the criteria:
A.${(dS)_{V,E}} = 0,{(dG)_{P,T}} = 0$
B.${(dS)_{V,E}} = 0,{(dG)_{P,T}} > 0$
C.${(dS)_{V,E}} < 0,{(dG)_{P,T}} < 0$
D.${(dS)_{V,E}} > 0,{(dG)_{P,T}} < 0$

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Last updated date: 13th Jun 2024
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Answer
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Hint:Reversible process: The reaction which can be only processed in one direction only i.e. either forward direction or backward direction, are known as reversible reactions.
Irreversible process: The reaction which can be only processed in both direction only i.e. forward direction as well as backward direction, are known as irreversible reactions.

Complete step by step answer:
First of all we will talk about the terms reversible, irreversible, Gibbs free energy and entropy.
Reversible process: The reaction which can be only processed in one direction only i.e. either forward direction or backward direction, are known as reversible reactions.
Irreversible process: The reaction which can be only processed in both direction only i.e. forward direction as well as backward direction, are known as irreversible reactions.
Spontaneous reaction: Those reactions which can proceed in a particular direction by their own without taking the help of external sources.
Non-spontaneous reaction: Those reactions which cannot proceed in a particular direction by their own. They need the help of external sources to proceed with the reaction.
Enthalpy: It is defined as the sum of internal energy and the product of pressure and volume, is known as enthalpy. It is represented by $H$. So according to the definition the enthalpy will be $H = U + PV$ where $U$ is internal energy, $P$ is the pressure and $V$ is the volume.
Entropy: It is defined as the measure of molecular disorder or randomness of a system.
Gibbs free energy: It is defined as the sum of enthalpy and the product of temperature with entropy of the system.
In a non-spontaneous reaction, Gibbs free energy is positive and energy is absorbed and change in entropy is negative. And for spontaneous reaction, Gibbs free energy is negative and change in entropy is positive.
So, in an irreversible process taking place at constant $T$ and $P$ and in which only pressure-volume work is being done the change in Gibbs free energy ($dG$) and change in entropy ($dS$) satisfy the criteria as ${(dS)_{V,E}} > 0,{(dG)_{P,T}} < 0$.


Note:Here the negative means less than zero and positive means greater than zero. The notation ${(dS)_{V,E}}$ means change in entropy and ${(dG)_{P,T}}$ means change in Gibbs free energy at constant pressure and temperature.