Question

We know for an irreversible process, dS>dq/T

.

And if the process is done at constant pressure we can take the equation as dH−TdS<0
.

And we defined Gibbs energy, G=H−TS
. At constant temperature and pressure dG≤0
.

But the fundamental equation of Gibbs energy dG
, in terms of temperature and pressure is given by dG=Vdp−SdT
.

And as per our original conditions, i.e. at constant pressure and temperature for an irreversible process the value dG
should be less than zero.

I cannot understand for the same condition the two equations give different answers.

Answer 1

The discrepancy arises due to misunderstanding the application of Gibbs energy equations; at constant temperature and pressure, irreversible processes generate additional entropy leading to a negative change in Gibbs free energy (∆G < 0), indicating spontaneity.

Step-by-step explanation:

The confusion arises from applying the fundamental differential form of Gibbs energy, dG = Vdp - SdT, under conditions of constant temperature (T) and pressure (p). At constant T and p, both dp and dT are zero, implying dG should be zero. However, this takes into account only reversible changes.

In an irreversible process, additional entropy is produced within the system, and this is not accounted for in the differential form of dG because it assumes reversible changes. For irreversible processes at constant T and p, the appropriate expression is ∆G = ∆H - T∆S, using the fact that ∆H = q and ∆S = qrev/T.

Because the actual entropy change (∆S) is greater than the reversible heat divided by temperature due to the production of entropy, the change in Gibbs free energy (∆G) becomes negative (∆G < 0), which reflects the spontaneous nature of the process.

Understanding this points to the principle that Gibbs free energy will decrease in any process occurring at constant T and p that is accompanied by an overall increase in the entropy of the universe. This is central in determining the spontaneity of a reaction, where a negative ∆G indicates a spontaneous process.

The concept of reversible processes is a theoretical construct to define the entropy change, which as a state function is the same for both reversible and irreversible processes leading to the same final state.

Therefore, in practical terms, an irreversible process at constant T and p will have a ∆G < 0, reflecting the inevitable production of entropy and thereby the tendency towards a more disordered or higher entropy state as guided by the second law of thermodynamics. It is this increase in entropy which underlies the decrease in Gibbs free energy signaling spontaneity.