Question

In an isolated system, find the condition for spontaneous reaction.
(A)- $\Delta U = 0,\Delta S = 0,\Delta G = 0$
(B)- $\Delta U < 0,\Delta S > 0,\Delta G < 0$
(C)- $\Delta U = 0,\Delta S > 0,\Delta G < 0$
(D)- $\Delta U < 0,\Delta S < 0,\Delta G < 0$

Answer 1

Hint: An isolated system can either be a physical system so far removed from other systems that it does not interact with them or it can also be a thermodynamic system enclosed by rigid immovable walls through which neither mass nor energy can pass.

Complete step by step solution:
In thermodynamics, a spontaneous process is the time-evolution of a system in which it releases free energy and it moves to a lower state i.e. more thermodynamically stable energy state.
As given in the options, we have three terms namely Internal energy denoted by U, Entropy which is denoted by S and Gibbs free energy which is denoted by G. Let's have a basic idea about them in order to pick the correct option.
- Internal energy (U) : The internal energy of a thermodynamic system is the energy which is contained within it. In other words, it is the energy necessary to create the system in any given internal state. The difference in internal energy is determined by thermodynamic processes that carry the system between the reference state and the current state of interest. In spontaneous condition it will become equals to zero.
- Entropy (S) : Entropy is an extensive property of any thermodynamic system. The second law of thermodynamics states that the entropy of an isolated system can never decrease over time. Isolated systems spontaneously evolve towards thermodynamic equilibrium i.e. the state with maximum entropy. Entropy is a function of state of the system, so the change in entropy of a system can be determined by its initial and final states. It is always greater than zero in spontaneous condition.
- Gibbs free energy(G) : Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of reversible work that may be performed by a system at a constant temperature and pressure. Since in spontaneous conditions entropy is positive so by the relation of Gibbs free energy and entropy it is clear that for the condition of spontaneity, Gibbs free energy will be less than zero.

From the above discussion, it is clear that the correct answer for the above question is option (C).

Note: Remember that the sign convention for free energy change follows the general convention for thermodynamic measurements, in which a release of free energy from the system is termed as a negative change in the free energy of the system and a positive change in the free energy of the surroundings and vice- versa.