[rajajidwivedi]

can you tell me about actual meaning of G in thermodynamics and how does it tell about useful work and why P :delta:V is non useful work.

[Aeon]

What is the mathematical definition of G?

Do you know what enthalpy and entropy are?

[rajajidwivedi]

yes i know that but what is physical significance of gibbs energy.

[Aeon]

First, define G.

Gibbs free energy is used as an indication of spontaneity. What values of G indicate spontaneous change will occur? Positive or negative?

[rajajidwivedi]

i know formula and mathematical derivation as well but i need to clear the physical meaning as entropy tells abt randomness.

[Aeon]

Erm...

Write down G. Answer these questions:

1) How can  :delta: G < 0?
2) How can  :delta: G > 0?
3) In what case is a reaction spontaneous?
4) In what case is a system in equilibrium?

Enthalpy is interpreted as (for an undergraduate, me being one) bonding strength.
Entropy is, like you mentioned, a measure of order.

P :delta: V can be useful (reversible). Consider a simple piston with no gas exit and volume V. If you compress it to V/2 and put an appropriate weight on top of it so the piston pushes it back to ~V, has the piston done useful work?