Name: Absolute Zero and Third Law of Thermodynamics
Uploaded: 2019-07-19
Duration: 20 min
Description: In this video, you will learn what absolute zero and the third law of thermodynamics is. You will also learn about the significance of the third law of therm...

Question

Starting with the thermodynamic relationships,

G = H - TS

, derive the following relationship:

ΔG = - {TΔS}_{total} .

Accepted Answer

The total entropy change when the system is not isolated from the surroundings is given by

$∆ S_{total} = ∆ S_{system} + ∆ S_{surroundings} - - - - - (i) .$

Then by definition of entropy change,

$∆ S_{surroundings} = \frac{- q_{p}}{T} - - - - - (ii) .$ (minus sign before q_p indicates that the heat is lost by the surroundings).

Further, we know that at constant pressure, $q_{p} = ∆ H$ .

Substituting this value in equation (ii), we get $∆ S_{surroundings} = \frac{- ∆ H}{T} - - - - - (iii) .$

Substituting this value in equation (i), we get $∆ S_{total} = ∆ S_{system} - \frac{∆ H}{T} - - - - - (iv) .$

We can write equation (iv) as, $∆ S_{total} = ∆ S - \frac{∆ H}{T} - - - - - (v) .$

Multiplying throughout by $T$ , we get $T ∆ S_{total} = T ∆ S_{system} - ∆ H - - - - - (vi) .$

But for a change taking place at constant temperature and pressure, $∆ G = ∆ H - T ∆ S - - - - - (vii) .$

Substituting this value in equation (vi), we get

$T ∆ S_{total} = - ∆ G . or ∆ G = - T ∆ S_{total} .$

Starting with the thermodynamic relationships, $G = H - TS$ , derive the following relationship: $ΔG = - {TΔS}_{total} .$

Important Questions on Thermodynamics

Learn and Prepare for any exam you want !

Starting with the thermodynamic relationships, G=H–TS, derive the following relationship: ΔG=–TΔStotal.

Important Questions on Thermodynamics

Learn and Prepare for any exam you want !

Starting with the thermodynamic relationships, $G = H - TS$ , derive the following relationship: $ΔG = - {TΔS}_{total} .$