Question

For a spontaneous process, the correct statements is(are)
(A) ${\left( {\vartriangle {{\text{G}}_{system}}} \right)_{T,P}} > 0$
(B) $\left( {\vartriangle {{\text{S}}_{system}}} \right) + \left( {\vartriangle {S_{surroundings}}} \right) > 0$
(C) ${\left( {\vartriangle {{\text{G}}_{system}}} \right)_{T,P}} < 0$
(D) ${\left( {\vartriangle {U_{system}}} \right)_{T,V}} > 0$

Answer 1

This question talks about the spontaneity of the process. It can be expressed by observing entropy change of the system and surrounding it together or by expressing free energy of the system alone at constant Pressure and Temperature.

Complete answer:
A Spontaneous process or a reaction is a process or reaction that considers the condition favourable at which the reaction is occurring. We take an example of fire burning, the reaction is exothermic, which results in decrease of energy of the system as energy is released in the surrounding as heat energy. Once the reaction becomes spontaneous it goes on until one of the reactants is finished. The products of a fire are generally consisting mostly of gases like carbon dioxide and water vapour, so the entropy is increased in most fire burning reactions like combustion.
We should also know about non-spontaneous processes. Non-spontaneous process is just opposite of spontaneous process; this process does not consider conditions favourable at which the process is occurring. Non-spontaneous processes or reactions are generally endothermic. Entropy in Non-spontaneous reactions are generally decreased.
Now what are the conditions in which a reaction or process is considered spontaneous. there are three conditions:
$\left( {\vartriangle {{\text{S}}_{system}}} \right) + \left( {\vartriangle {S_{surroundings}}} \right) > 0$
Sum of entropy change of system $\vartriangle {{\text{S}}_{system}}$ , and entropy change of surroundings $\vartriangle {{\text{S}}_{system}}$ must be positive.
${\left( {\vartriangle {{\text{G}}_{system}}} \right)_{T,P}} < 0$
Gibbs free energy change $\vartriangle {{\text{G}}_{system}}$ , in the system must be negative.
${\left( {\vartriangle {U_{system}}} \right)_{T,V}} < 0$
Change in internal energy of the system must be negative.
So, options (B) and (C) are correct.

Note:
We should be clear about one thing: spontaneous process or reaction does not mean reaction occurring fast or product is forming fast, even if the rate of formation of product is less, the spontaneous reaction will favour the formation of product.